First slide

Simple hormonic motion

Question

A 4kg roller is attached to a massless spring of spring constant k = 100N/m. It rolls without slipping along a frictionless horizontal road. The roller is displaced from its equilibrium position by l0cm and then released. Its maximum speed will be

Moderate

A

0.5 ms^–1
B

0.6 ms^–1
C

0.4 ms^–1
D

0.8 ms^–1

Solution

Kinetic energy of the roller = $\large \frac{1}{2}m{v^2} + \frac{1}{2}{I_c}{\omega ^2}$
$\large = \,\frac{1}{2}m{v^2} + \frac{1}{2}m{r^2} \times {\left( {\frac{v}{r}} \right)^2}$
$\large \, = \,\frac{3}{4}m{v^2}$
$\large \therefore \,\frac{3}{4}m{V^2}_{\max }\, = \,\frac{1}{2}K{A^2}$
$\large \Rightarrow \,{V_{\max }}\, = \,A\sqrt {\frac{{2k}}{{3m}}}$
$\large \Rightarrow \,{V_{\max }}\, = \,0.1 \times \sqrt {\frac{{2 \times 100}}{{3 \times 4}}} \,m/s$
= 0.4 m/s

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