Question

A 1.00 kg block is attached to a spring with spring constant 13.5 N/m . While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 33.0 cm/s . What is the block's speed at the point where x= 0.450 A?

Answer 1

here,

the mass of block , m = 1 kg

the spring constant , K = 13.5 N/m

the maximum speed , vm = 33 cm/s = 0.33 m/s

let the amplitude of motion be A

using conservation of energy

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

1 * 0.33^2 = 13.5 * A^2

A = 0.0898 m

let the speed of block be v1 at x1 = 0.45 A

using conservation of energy

0.5 * K * A^2 = 0.5 * K * x1^2 + 0.5 * m * v1^2

0.5 * 13.5 * A^2 * (1 - 0.45^2) = 0.5 * 1 * v1^2

0.5 * 13.5 * 0.0898^2 * (1 - 0.45^2) = 0.5 * 1 * v1^2

solving for v1

v1 = 0.29 m/s

the speed of block at this point is 0.29 m/s