First slide

Simple hormonic motion

Question

A uniform circular disc of mass 12kg is held by two identical springs as shown in the figure. When the disc is pressed down slightly and released, it executes SHM with a time period of 2 sec. The force constant of each spring is:

Moderate

A

236 Nm^–1
B

118.3 Nm^–1
C

59.15 Nm^–1
D

None of the above

Solution

As the two springs are connected in parallel keff = 2k
$\large \therefore T\, = \,2\pi \sqrt {\frac{M}{k}} \, \Rightarrow 2 = 2\pi \sqrt {\frac{{12}}{{2k}}} \, \Rightarrow \frac{1}{{{\pi ^2}}}\, = \,\frac{6}{k}$
$\large k\, = \,6{\pi ^2}\, = \,59.15N/m$

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