Question

A 0.750 kg block is attached to a spring with spring constant 16 N/m . While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 37 cm/s

What is the amplitude of the subsequent oscillations?

What is the block's speed at the point where x=0.25A?

Answer 1

here,

the mass of block , m = 0.75 kg

spring constant , K = 16 N/m

maximum speed , vm = 37 cm/s = 0.37 m/s

let the amplitude of oscillation be A

using conservation of energy

0.5 * K * A^2 = 0.5 * m * vm^2

16 * A^2 = 0.75 * 0.37^2

solving for A

A = 0.08 m = 8 cm

the amplitude of motion is 8 cm

let the block speed be v at x = 0.25 A

using conservation of energy

0.5 * m * vm^2 = 0.5 * m * v^2 + 0.5 * K * x^2

0.5 * m * vm^2 = 0.5 * m * v^2 + 0.5 * K * (0.25 * A)^2

0.75 * 0.37^2 = 0.75 * v^2 + 0.5 * 16 * (0.25 * 0.08)^2

solving for v

v = 0.36 m/s

the speed of block is 0.36 m/s