A small block is attached to an ideal spring and is moving in SHM on a horizontal, frictionless surface. The amplitude of the motion is 0.250 m and the period is 3.20 s. What are the speed and acceleration of the block when x = 0.160 m?

Solution 24E Step 1: Amplitude of the motion A = 0.25 m Period T = 3.20 s Displacement x = 0.16 m Step 2: To find the speed and acceleration of the block From conservation of energy 1mv + kx 1 2 = kA ----(1) 2 x 2 2 Simplifying the above equation, we can get the expression for speed 2 2 2 mv x = kA - kx 2 2 v x = k(A x ) m k 2 2 v x= m (A x -----(2)