Question

A 1.40 kg block is attached to a spring with spring constant 16.0 N/m . While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 44.0 cm/s . What are...

A. The amplitude of the subsequent oscillations?

B. The block's speed at the point where x= 0.150 A?

Answer 1

here,

mass of the block , m = 1.4 kg

spring constant , k = 16 N/m

initial speed , v = 44 cm/s

v = 0.44 m/s

A)

let the amplitude be A

using conservation of energy

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

16 * A^2 = 1.4 * 0.44^2

A = 0.13 m

the amplitude of the oscillation is 0.13 m

B)

let the block speed be v1 at x1 = 0.15 * A = 0.0195 m

using conservation of energy

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

1.4 * v1^2 = 16 * ( 0.13^2 - 0.0195^2)

v1 = 0.43 m/s

the speed of block is 0.43 m/s