Repeat Exercise 14.13, but assume that at t = 0 the block has velocity - 4.00 m > s and displacement + 0.200 m. 14.13 . A 2.00-kg, frictionless block is attached to an ideal spring with force constant 300 N/m. At t = 0 the spring is neither stretched nor compressed and the block is moving in the negative direction at 12.0 m/s. Find (a) the amplitude and (b) the phase angle. (c) Write an equation for the position as a function of time.
Solution 12E Introduction We have to calculate the amplitude A, phase angle . Then we have to write the equation of motion. Step 1 (a) The total energy at the given time is the kinetic energy of the mass plus the potential energy of the spring. Hence the initial energy of the system is E = k2 + mv 2 2 Now if A is the amplitude then we have 1 2 E = k2 So we have 2kA = k2 + mv 2 2 A = kx +mv k (350 N/m)(0.200 m) +(2.00 kg)(4.00 m/s) = 350 N/m = 0.363 m So the amplitude of the motion is 0.363 m.