Suppose a 32-pound weight stretches a spring 2 feet. If

A beam is embedded at its left end and simply supported at its right end. Find the deflection y(x) when the load is as given in Problem 77.

In Problems 1– 20 find either F(s) or f (t), as indicated. \(\mathscr{L}\left\{t e^{10 t}\right\}\) Text Transcription: L{te^10t}

In Problems 1– 20 find either F(s) or f (t), as indicated. \(\mathscr{L}\left\{t^{3} e^{-2 t}\right\}\) Text Transcription: L{t^3e^-2t}

In Problems 1– 20 find either F(s) or f (t), as indicated. \(\mathscr{L}\left\{t e^{-6 t}\right\}\) Text Transcription: L{te^-6t}

In Problems 1– 20 find either F(s) or f (t), as indicated. \(\mathscr{L}\left\{t\left(e^{t}+e^{2 t}\right)^{2}\right\}\) Text Transcription: L{t(e^t + e^2t)^2}

In Problems 1– 20 find either F(s) or f (t), as indicated. \(\mathscr{L}\left\{t^{10} e^{-7 t}\right\}\) Text Transcription: L{t^10e^-7t}

In Problems 1– 20 find either F(s) or f (t), as indicated. \(\mathscr{L}\left\{e^{2 t}(t-1)^{2}\right\}\) Text Transcription: L{e^2t(t - 1)^2}

In Problems 1– 20 find either F(s) or f (t), as indicated. \(\mathscr{L}\left\{e^{t} \sin 3 t\right\}\) Text Transcription: L{e^t sin 3t}

In Problems 1– 20 find either F(s) or f (t), as indicated. \(\mathscr{L}^{-1}\left\{\frac{1}{(s-1)^{4}}\right\}\) Text Transcription: L^-1{1/(s - 1)^4}

In Problems 1– 20 find either F(s) or f (t), as indicated. \(\mathscr{L}^{-1}\left\{\frac{1}{(s+2)^{3}}\right\}\) Text Transcription: L^-1{1/(s +2)^3}

In Problems 1– 20 find either F(s) or f (t), as indicated. \(\mathscr{L}^{-1}\left\{\frac{1}{s^{2}-6 s+10}\right\}\) Text Transcription: L^-1{1/s^2 - 6s + 10}

In Problems 1– 20 find either F(s) or f (t), as indicated. \(\mathscr{L}\left\{e^{-2 t} \cos 4 t\right\}\) Text Transcription: L{e^-2t cos 4t}

In Problems 1– 20 find either F(s) or f (t), as indicated. \(\mathscr{L}\left\{\left(1-e^{t}+3 e^{-4 t}\right) \cos 5 t\right\}\) Text Transcription: L{(1 - e^t + 3e^-4t) cos 5t}

In Problems 1– 20 find either F(s) or f (t), as indicated. \(\mathscr{L}\left\{e^{3 t}\left(9-4 t+10 \sin \frac{t}{2}\right)\right\}\) Text Transcription: L{e^3t(9 - 4t + 10 sin t/2)}

In Problems 1– 20 find either F(s) or f (t), as indicated. \(\mathscr{L}^{-1}\left\{\frac{s}{s^{2}+4 s+5}\right\}\) Text Transcription: L^-1{s/s^2 + 4s + 5}

In Problems 1– 20 find either F(s) or f (t), as indicated. \(\mathscr{L}^{-1}\left\{\frac{2 s+5}{s^{2}+6 s+34}\right\}\) Text Transcription: L^-1{2s + 5/s^2 + 6s + 34}

In Problems 1– 20 find either F(s) or f (t), as indicated. \(\mathscr{L}^{-1}\left\{\frac{1}{s^{2}+2 s+5}\right\}\) Text Transcription: L^-1{1/s^2 + 2s + 5}

In Problems 1– 20 find either F(s) or f (t), as indicated. \(\mathscr{L}^{-1}\left\{\frac{s}{(s+1)^{2}}\right\}\) Text Transcription: L^-1{s/(s +1)^2}

In Problems 1– 20 find either F(s) or f (t), as indicated. \(\mathscr{L}^{-1}\left\{\frac{2 s-1}{s^{2}(s+1)^{3}}\right\}\) Text Transcription: L^1{2s - 1/ s^2(s + 1)^3}

In Problems 1– 20 find either F(s) or f (t), as indicated. \(\mathscr{L}^{-1}\left\{\frac{(s+1)^{2}}{(s+2)^{4}}\right\}\) Text Transcription: L^-1{(s + 1)^2/(s + 2)^4}

In Problems 21– 30 use the Laplace transform to solve the given initial-value problem. \(y^{\prime}+4 y=e^{-4 t}\), y(0) = 2 Text Transcription: y^prime + 4y = e^-4t

In Problems 1– 20 find either F(s) or f (t), as indicated. \(\mathscr{L}^{-1}\left\{\frac{5 s}{(s-2)^{2}}\right\}\) Text Transcription: L^1{5s/(s - 2)^2}

In Problems 21– 30 use the Laplace transform to solve the given initial-value problem. \(y^{\prime}-y=1+t e^{t}\), y(0) = 0 Text Transcription: y^prime - y = 1 + te^t

In Problems 21– 30 use the Laplace transform to solve the given initial-value problem. \(y^{\prime \prime}+2 y^{\prime}+y=0\), y(0) =1, \(y^{\prime}(0)=1\) Text Transcription: y^prime.prime + 2y^prime + y = 0 y^prime(0) = 1

In Problems 21– 30 use the Laplace transform to solve the given initial-value problem. \(y^{\prime \prime}-4 y^{\prime}+4 y=t^{3} e^{2 t}\) \(y^{\prime}(0)=0\) Text Transcription: y^prime - 4y^prime + 4y = t^3e^2t y^prime(0) = 0

In Problems 21– 30 use the Laplace transform to solve the given initial-value problem. \(y^{\prime \prime}-6 y^{\prime}+9 y=t\), y(0) = 0, \(y^{\prime}(0)=1\) Text Transcription: y^prime.prime - 6y^prime + 9y = t y^prime(0) = 1

In Problems 21– 30 use the Laplace transform to solve the given initial-value problem. \(y^{\prime \prime}-6 y^{\prime}+13 y=0\), y(0) = 0, \(y^{\prime}(0)=-3\) Text Transcription: y^prime.prime - 6y^prime + 13 = 0 y^prime(0)= -3

In Problems 21– 30 use the Laplace transform to solve the given initial-value problem. \(y^{\prime \prime}-2 y^{\prime}+5 y=1+t\), y(0) = 0, \(y^{\prime}(0)=4\) Text Transcription: y^prime.prime = 2y^prime + 5y = 1 + t y^prime(0) = 4

In Problems 21– 30 use the Laplace transform to solve the given initial-value problem. \(y^{\prime \prime}-4 y^{\prime}+4 y=t^{3}\), y(0) = 1, \(y^{\prime}(0)=0\) Text Transcription: y^prime = 4y^prime + 4y = t^3 y^prime(0) = 0

In Problems 21– 30 use the Laplace transform to solve the given initial-value problem. \(2 y^{\prime \prime}+20 y^{\prime}+51 y=0\), y(0) = 2, \(y^{\prime}(0)=0\) Text Transcription: 2y^prime.prime + 20y^prime + 51y = 0 y^prime(0) = 0

In Problems 21– 30 use the Laplace transform to solve the given initial-value problem. \(y^{\prime \prime}-y^{\prime}=e^{t} \cos t\), y(0) = 0, \(y^{\prime}(0)=0\) Text Transcription: y^prime.prime - y^prime = e^t cos t y^prime(0) = 0

In Problems 31 and 32 use the Laplace transform and the procedure outlined in Example 10 to solve the given boundary-value problem. \(y^{\prime \prime}+8 y^{\prime}+20 y=0\), y(0) = 0, \(y^{\prime}(\pi)=0\) Text Transcription: y^prime.prime + 8y^prime + 20y = 0 y^prime(pi) = 0

In Problems 31 and 32 use the Laplace transform and the procedure outlined in Example 10 to solve the given boundary-value problem. \(y^{\prime \prime}+2 y^{\prime}+y=0\), \(y^{\prime}(0)=2\), y(1) = 2 Text Transcription: y^prime.prime + 2y^prime + y = 0 y^prime(0) = 2

A 4-pound weight stretches a spring 2 feet. The weight is released from rest 18 inches above the equilibrium position, and the resulting motion takes place in a medium offering a damping force numerically equal \(\frac{7}{8}\) to times the instantaneous velocity. Use the Laplace transform to find the equation of motion x(t) Text Transcription: 7/8

Use the Laplace transform to find the charge q(t) in an RC series circuit when q(0) = 0 and \(E(t)=E_{0} e^{-k t}\), k 0. Consider two cases: \(k \neq 1 / R C\) and k = 1RC. Text Transcription: E(t) = E_0e^-kt k neq 1/RC

In Problems 37 – 48 find either F(s) or f (t), as indicated. \(\mathscr{L}\{(t-1) \mathscr{U}(t-1)\}\) Text Transcription: L{(t - 1) U(t - 1)}

In Problems 37 – 48 find either F(s) or f (t), as indicated. \(\mathscr{L}\left\{e^{2-t} \mathscr{U}(t-2)\right\}\) Text Transcription: L{e^2-t U(t -2)}

Recall that the differential equation for the instantaneous charge q(t) on the capacitor in an LRC-series circuit is given by \(L \frac{d^{2} q}{d t^{2}}+R \frac{d q}{d t}+\frac{1}{C} q=E(t)\). (20) See Section 5.1. Use the Laplace transform to find q(t) when L = 1 h, \(R=20 \Omega\), C = 0.005 f, E(t) = 150 V, t 0, q(0) = 0, and i(0) = 0. What is the current i(t)? Text Transcription: L d^2q/dt^2 + R dq/dt + 1/C q = E(t) R = 20 Omega

In Problems 37 – 48 find either F(s) or f (t), as indicated. \(\mathscr{L}\{t \mathscr{U}(t-2)\}\) Text Transcription: L{t U(t - 2)}

Consider a battery of constant voltage \(E_{0}\) that charges the capacitor shown in Figure 7.3.9. Divide equation (20) by L and define \(2 \lambda=R / L\) and \(\omega^{2}=1 / L C\). Use the Laplace transform to show that the solution q(t) of \(q^{\prime \prime}+2 \lambda q^{\prime}+\omega^{2} q=E_{0} / L\)subject to q(0) = 0, i(0) = 0 is Text Transcription: E_0 2lambda = R/L omega^2 = 1/LC q^prime.prime + 2lambda q^prime + omega^2q = E_0/L

In Problems 37 – 48 find either F(s) or f (t), as indicated. \(\mathscr{L}\{(3 t+1) \mathscr{U}(t-1)\}\) Text Transcription: L{(3t + 1) U(t - 1)}

In Problems 37 – 48 find either F(s) or f (t), as indicated. \(\mathscr{L}^{-1}\left\{\frac{e^{-2 s}}{s^{3}}\right\}\) Text Transcription: L^-1{e^-2s/s^3}

In Problems 37 – 48 find either F(s) or f (t), as indicated. \(\mathscr{L}\{\cos 2 t \mathscr{U}(t-)\}\) Text Transcription: L{cos 2t U(t -)}

In Problems 37 – 48 find either F(s) or f (t), as indicated. \(\mathscr{L}\left\{\sin t \mathscr{U}\left(t-\frac{}{2}\right)\right\}\) Text Transcription: L{sin t U(t - /2)}

In Problems 37 – 48 find either F(s) or f (t), as indicated. \(\mathscr{L}^{-1}\left\{\frac{\left(1+e^{-2 s}\right)^{2}}{s+2}\right\}\) Text Transcription: L^-1{(1 + e^-2s)^2/s + 2}

In Problems 37 – 48 find either F(s) or f (t), as indicated. \(\mathscr{L}^{-1}\left\{\frac{e^{-s}}{s^{2}+1}\right\}\) Text Transcription: L^-1{e^-s/s^2 + 1}

In Problems 49 – 54 match the given graph with one of the functions in (a)–(f ). The graph of f (t) is given in Figure 7.3.10. (a) \(f(t)-f(t) \mathscr{U}(t-a)\) (b) \(f(t-b) \mathscr{U}(t-b)\) (c) \(f(t) \mathscr{U}(t-a)\) (d) \(f(t)-f(t) \mathscr{U}(t-b)\) (e) \(f(t) \mathscr{U}(t-a)-f(t) \mathscr{U}(t-b)\) (f) \(f(t-a) \mathscr{U}(t-a)-f(t-a) \mathscr{U}(t-b)\) Text Transcription: f(t) - f(t) U(t - a) f(t - b) U(t - b) f(t) U(t - a) f(t) - f(t) U(t -b) f(t) u(t - a) - f(t) u(t - b) f(t - a) u(t - a) - f(t - a) u(t - b)

In Problems 49 – 54 match the given graph with one of the functions in (a)–(f ). The graph of f (t) is given in Figure 7.3.10. (a) \(f(t)-f(t) \mathscr{U}(t-a)\) (b) \(f(t-b) \mathscr{U}(t-b)\) (c) \(f(t) \mathscr{U}(t-a)\) (d) \(f(t)-f(t) \mathscr{U}(t-b)\) (e) \(f(t) \mathscr{U}(t-a)-f(t) \mathscr{U}(t-b)\) (f) \(f(t-a) \mathscr{U}(t-a)-f(t-a) \mathscr{U}(t-b)\) Text Transcription: f(t) - f(t) U(t - a) f(t - b) U(t - b) f(t) U(t - a) f(t) - f(t) U(t -b) f(t) u(t - a) - f(t) u(t - b) f(t - a) u(t - a) - f(t - a) u(t - b)

In Problems 49 – 54 match the given graph with one of the functions in (a)–(f ). The graph of f (t) is given in Figure 7.3.10. (a) \(f(t)-f(t) \mathscr{U}(t-a)\) (b) \(f(t-b) \mathscr{U}(t-b)\) (c) \(f(t) \mathscr{U}(t-a)\) (d) \(f(t)-f(t) \mathscr{U}(t-b)\) (e) \(f(t) \mathscr{U}(t-a)-f(t) \mathscr{U}(t-b)\) (f) \(f(t-a) \mathscr{U}(t-a)-f(t-a) \mathscr{U}(t-b)\) Text Transcription: f(t) - f(t) U(t - a) f(t - b) U(t - b) f(t) U(t - a) f(t) - f(t) U(t -b) f(t) u(t - a) - f(t) u(t - b) f(t - a) u(t - a) - f(t - a) u(t - b)

In Problems 49 – 54 match the given graph with one of the functions in (a)–(f ). The graph of f (t) is given in Figure 7.3.10. (a) \(f(t)-f(t) \mathscr{U}(t-a)\) (b) \(f(t-b) \mathscr{U}(t-b)\) (c) \(f(t) \mathscr{U}(t-a)\) (d) \(f(t)-f(t) \mathscr{U}(t-b)\) (e) \(f(t) \mathscr{U}(t-a)-f(t) \mathscr{U}(t-b)\) (f) \(f(t-a) \mathscr{U}(t-a)-f(t-a) \mathscr{U}(t-b)\) Text Transcription: f(t) - f(t) U(t - a) f(t - b) U(t - b) f(t) U(t - a) f(t) - f(t) U(t -b) f(t) u(t - a) - f(t) u(t - b) f(t - a) u(t - a) - f(t - a) u(t - b)

In Problems 49 – 54 match the given graph with one of the functions in (a)–(f ). The graph of f (t) is given in Figure 7.3.10. (a) \(f(t)-f(t) \mathscr{U}(t-a)\) (b) \(f(t-b) \mathscr{U}(t-b)\) (c) \(f(t) \mathscr{U}(t-a)\) (d) \(f(t)-f(t) \mathscr{U}(t-b)\) (e) \(f(t) \mathscr{U}(t-a)-f(t) \mathscr{U}(t-b)\) (f) \(f(t-a) \mathscr{U}(t-a)-f(t-a) \mathscr{U}(t-b)\) Text Transcription: f(t) - f(t) U(t - a) f(t - b) U(t - b) f(t) U(t - a) f(t) - f(t) U(t -b) f(t) u(t - a) - f(t) u(t - b) f(t - a) u(t - a) - f(t - a) u(t - b)

In Problems 55 – 62 write each function in terms of unit step functions. Find the Laplace transform of the given function. \(f(t)=\left\{\begin{array}{lr} 2, & 0 \leq t<3 \\ -2, & t \geq 3 \end{array}\right. \) Text Transcription: f(t) = { 2, 0 leq t < 3 -2, t geq 3

In Problems 55 – 62 write each function in terms of unit step functions. Find the Laplace transform of the given function. \(f(t)=\left\{\begin{array}{lr} 1, & 0 \leq t<4 \\ 0, & 4 \leq t<5 \\ 1, & t \geq 5 \end{array}\right. \) Text Transcription: f(t) = {1, 0 leq t < 4 0, 4 leq t < 5 1, t geq 5

In Problems 55 – 62 write each function in terms of unit step functions. Find the Laplace transform of the given function. \(f(t)=\left\{\begin{array}{lr} 0, & 0 \leq t<1 \\ t^{2}, & t \geq 1 \end{array}\right. \) Text Transcription: f(t) = {0, 0 leq t < 1 t^2, t geq 1

In Problems 55 – 62 write each function in terms of unit step functions. Find the Laplace transform of the given function. \(f(t)=\left\{\begin{array}{lr} 0, & 0 \leq t<3 / 2 \\ \sin t, & t \geq 3 \end{array}\right. \) Text Transcription: f(t) = {0, 0 leq 5< 3 /2 sin t, t geq 3 /2

In Problems 55 – 62 write each function in terms of unit step functions. Find the Laplace transform of the given function. \(f(t)=\left\{\begin{array}{lr} t, & 0 \leq t<2 \\ 0, & t \geq 2 \end{array}\right. \) Text Transcription: f(t) = {t, 0 leq t < 2 0, t geq 2

In Problems 49 – 54 match the given graph with one of the functions in (a)–(f ). The graph of f (t) is given in Figure 7.3.10. (a) \(f(t)-f(t) \mathscr{U}(t-a)\) (b) \(f(t-b) \mathscr{U}(t-b)\) (c) \(f(t) \mathscr{U}(t-a)\) (d) \(f(t)-f(t) \mathscr{U}(t-b)\) (e) \(f(t) \mathscr{U}(t-a)-f(t) \mathscr{U}(t-b)\) (f) \(f(t-a) \mathscr{U}(t-a)-f(t-a) \mathscr{U}(t-b)\) Text Transcription: f(t) - f(t) U(t - a) f(t - b) U(t - b) f(t) U(t - a) f(t) - f(t) U(t -b) f(t) u(t - a) - f(t) u(t - b) f(t - a) u(t - a) - f(t - a) u(t - b)

In Problems 55 – 62 write each function in terms of unit step functions. Find the Laplace transform of the given function. \(f(t)=\left\{\begin{array}{lr} \sin t, & 0 \leq t<2 \\ 0, & t \geq 2 \end{array}\right. \) Text Transcription: f(t) = {sin t, 0 leq t < 2 0, t geq 2

In Problems 55 – 62 write each function in terms of unit step functions. Find the Laplace transform of the given function.

In Problems 55 – 62 write each function in terms of unit step functions. Find the Laplace transform of the given function.

In Problems 63–70 use the Laplace transform to solve the given initial-value problem. \(y^{\prime}+y=f(t)\), y(0) = 0, where \(f(t)=\left\{\begin{array}{lr} 0, & 0 \leq t<1 \\ 5, & t \geq 1 \end{array}\right. \) Text Transcription: y^prime + f(t) f(t) = {0, 0 leq t < 1 5, t geq 1

In Problems 63–70 use the Laplace transform to solve the given initial-value problem. \(y^{\prime}+y=f(t)\), y(0) = 0, where \(f(t)=\left\{\begin{array}{crr} 1, & 0 \leq t & <1 \\ -1, & & t \geq 1 \end{array}\right. \) Text Transcription: y^prime + y = f(t), y(0) = 0, where \(f(t)=\left\{\begin{array}{cr} 1, & 0 \leq t<1 \\ -1, & t \geq 1 \end{array}\right. \) Text Transcription: y^prime + y = f(t) f(t) = {1, 0 leq t < 1 -1, t geq 1

In Problems 63–70 use the Laplace transform to solve the given initial-value problem. \(y^{\prime \prime}+4 y=f(t)\), y(0) = 0, \(y^{\prime}(0)=-1\), where \(f(t)=\left\{\begin{array}{lr} 1, & 0 \leq t<1 \\ 0, & t \geq 1 \end{array}\right. \) Text Transcription: y^prime + 4y = f(t) y^prime(0) = -1 f(t) = {1, 0 leq t < 1 0, t geq 1

In Problems 63–70 use the Laplace transform to solve the given initial-value problem. \(y^{\prime \prime}+4 y=\sin t \mathscr{U}(t-2)\), y(0) = 1, \(y^{\prime}(0)=0\) Text Transcription: y^prime.prime + 4y = sin t U(t - 2) y^prime(0) = 0

In Problems 63–70 use the Laplace transform to solve the given initial-value problem. \(y^{\prime \prime}-5 y^{\prime}+6 y=\mathscr{U}(t-1)\), y(0) = 0, \(y^{\prime}(0)=1\) Text Transcription: y^prime.prime - 5y^prime + 6y = u(t - 1) y^prime(0) = 1

In Problems 63–70 use the Laplace transform to solve the given initial-value problem. \(y^{\prime \prime}+y=f(t)\), y(0) = 0, \(y^{\prime}(0)=1\), where \(f(t)=\left\{\begin{array}{lr} 0, & 0 \leq t< \\ 1, & \leq t<2 \\ 0, & t \geq 2 \end{array}\right. \) Text Transcription: y^prime.prime + y = f(t) y^prime(0) = 1 f(t) = {0, 0 leq t < 1, leq t < 2 0, t geq 2

In Problems 63–70 use the Laplace transform to solve the given initial-value problem. \(y^{\prime}+2 y=f(t)\), y(0) = 0, where \(f(t)=\left\{\begin{array}{lr} t, & 0 \leq t<1 \\ 0, & t \geq 1 \end{array}\right. \) Text Transcription: y^prime + 2y = f(t) f(t) = {t, 0 leq t < 1 0, t geq 1

In Problems 63–70 use the Laplace transform to solve the given initial-value problem. \(y^{\prime \prime}+4 y^{\prime}+3 y=1-\mathscr{U}(t-2)-\mathscr{U}(t-4)+\mathscr{U}(t-6)\), y(0) = 0, \(y^{\prime}(0)=0\) Text Transcription: y^prime.prime + 4y^prime + 3y = 1 - U(t - 2) - U(t - 4) + U(t - 6) y^prime(0) = 0

Solve Problem 71 if the impressed force f(t) = sin t acts on the system for \(0 \leq t<2 \pi\) and is then removed. Text Transcription: 0 leq 5 < 2pi

In Problems 73 and 74 use the Laplace transform to find the charge q(t) on the capacitor in an RC-series circuit subject to the given conditions. q(0) = 0, \(R=2.5 \Omega\), C = 0.08 f, E(t) given in Figure 7.3.19 Text Transcription: R = 2.5Omega

(a) Use the Laplace transform to find the charge q(t) on the capacitor in an RC-series circuit when q(0) = 0, \(R=50 \Omega\), C = 0.01 f, and E(t) is as given in Figure 7.3.22. (b) Assume that \(E_{0}=100 \mathrm{V}\). Use a computer graphing program to graph q(t) for \(0 \leq t \leq 6\). Use the graph to estimate \(q_{\max }\), the maximum value of the charge. Text Transcription: R = 50 Omega E_0 = 100 V 0 leq t leq 6 q_max

(a) Use the Laplace transform to find the current i(t) in a single-loop LR-series circuit when i(0) = 0, L = 1h, \(R=10 \Omega\), and E(t) is as given in Figure 7.3.21. (b) Use a computer graphing program to graph i(t) for \(0 \leq t \leq 6\). Use the graph to estimate \(i_{\max }\) and \(i_{\min }\), the maximum and minimum values of the current. Text Transcription: R = 10 Omega 0 leq t leq 6 i_max i_min

In Problems 73 and 74 use the Laplace transform to find the charge q(t) on the capacitor in an RC-series circuit subject to the given conditions. \(q(0)=q_{0}\), \(R=10 \Omega\), C = 0.1 f, E(t) given in Figure 7.3.20 Text Transcription: q(0) = q_0 R = 10Omega

Suppose a 32-pound weight stretches a spring 2 feet. If the weight is released from rest at the equilibrium position, find the equation of motion x(t) if an impressed force f(t) = 20t acts on the system for \(0 \leq t<5\) and is then removed (see Example 5). Ignore any damping forces. Use a graphing utility to graph x(t) on the interval [0, 10]. Text Transcription: 0 leq t < 5

A cantilever beam is embedded at its left end and free at its right end. Use the Laplace transform to find the deflection y(x) when the load is given by \(w(x)=\left\{\begin{array}{lc} w_{0}, & 0<x<L / 2 \\ 0, & L / 2 \leq x<L \end{array}\right. \) Text Transcription: w(x) = {w_0, 0<x<L/2 0, L/2 leq x<l

Solve Problem 77 when the load is given by \(w(x)=\left\{\begin{array}{cr} 0, & 0<x<L / 3 \\ w_{0}, & L / 3<x<2 L / 3 \\ 0, & 2 L / 3<x<L \end{array}\right. \). Text Transcription: w(x) - {0, 0 < x < L/3 w_0, L/3 < x < 2L/3 0, 2L/3 < x < L

Find the deflection y(x) of a cantilever beam embedded at its left end and free at its right end when the load is as given in Example 10.

In Problems 37 – 48 find either F(s) or f (t), as indicated. \(\mathscr{L}^{-1}\left\{\frac{s e^{-s / 2}}{s^{2}+4}\right\}\) Text Transcription: L^-1{se^-s/2 / s^2 + 4}

In Problems 37 – 48 find either F(s) or f (t), as indicated. \(\mathscr{L}^{-1}\left\{\frac{e^{-s}}{s(s+1)}\right\}\) Text Transcription: L^-1{e^-s/s(s + 1)}

In Problems 37 – 48 find either F(s) or f (t), as indicated. \(\mathscr{L}^{-1}\left\{\frac{e^{-2 s}}{s^{2}(s-1)}\right\}\) Text Transcription: L^-1{e^-2s/s^2(s - 1)}