A 150 block attached to a spring with spring constant 3.0 oscillates horizontall

Question

A 150 block attached to a spring with spring constant 3.0 oscillates horizontally on a frictionless table. Its velocity is 20 when = -5.5 .

A.What is the amplitude of oscillation?

B.What is the block's maximum acceleration?

C.What is the block's position when the acceleration is maximum?

Explanation / Answer

(A) let a be the amplitude of oscillation. energy should be conserved. => for the given position energy = energy at max compression or expansion => 1/2 mv^2 + 1/2 kx^2 = 1/2 ka^2 m= 150g = 0.15kg, k=3. => a = 7.088 (B) max acceleration = max force/ mass max force at max compression or max expansion => max force = ka = 3x7.088 = 21.266 N => amax = 21.266/0.15 = 141.77 m/s^2. (c) block's position will be either max compression or max expansion.

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