Question

A 1.35 kg block is attached to a spring with spring constant 18.0 N/m . While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 50.0 cm/s . What are

a) the amplitude of the subsequent oscillations?

b) the block's speed at the point where x=0.350 A?

Answer 1

Given,

mass m = 1.35 kg

k = 18 N/m

k = m?²

18 = 1.35 ?²

? = 3.65

velocity at mean positon will be V_max = A ?

                                          0.50 = A *3.65

amplitude A = 0.137 m = 13.7 cm

b) at x= 0.35 A,

velocity, V = ? * ?A² - 0.35 A² = ? * A * ? 1- 0.35 ²

                   = 0.5 * 0.94

V = 0.47 m/s = 47 cm/s