Question

A 180 g mass on a smooth surface is attached to a horizontal spring with a spring constant 8 N m-1. The mass is set to oscillate by pulling it 5.0 cm from its equilibrium position and released. 

a) Calculate the period of the oscillation.

[ 1 mark ]

b) Calculate the maximum speed of the mass. 

[ 2 marks ]

c) Calculate the maximum acceleration of the mass 

[ 2 marks ]

Answer 1

Given:

$m=0.180\:\rm kg$

$k=8\:\rm N/m$

$A=5.0\:\rm cm$

a) the period of the oscillation

$$T=2\pi\sqrt{\frac{m}{k}}=6.48\sqrt{\frac{0.180}{8}}=0.942\:\rm s$$

b) the maximum speed of the mass

$$v_{\max}=A\omega =\frac{2\pi A}{T}=\frac{6.28*5.0}{0.942}=33.3\:\rm cm/s$$

c) the maximum acceleration of the mass

$$a_{\max}=v_{\max}\omega =\frac{2\pi v_{\max}}{T}=\frac{6.28*33.3}{0.942}=222\:\rm cm/s^2$$