A 16 kg block is attached to a spring with spring constant 1

A 1.6 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 38 cm/s.

(a) What is the amplitude of the subsequent oscillations?

cm

(b) What is the block\'s speed at the point where x = 1/3 A?

cm/s

Solution

a)

angular frequency

W=sqrt[K/m] =sqrt[16/1.6]

W=3.16 rad/s

Amplitude

A=V_max/W =0.38/3.16

A=12 cm

b)

By Conservation of energy

(1/2)KA² =(1/2)mV²+(1/2)Kx²

(1/2)KA²=(1/2)mV²+(1/2)K(A/3)²

(8/9)KA² =(1/2)mV²

(8/9)*16*0.12²=(1/2)*1.6*V²

V=0.506 m/s =50.6 cm/s