First slide

Applications of SHM

Question

A weightless spring of length 60 cm and force constant 200 N/m is kept straight and unstretched on a smooth horizontal table and its ends are rigidly fixed. A mass of 0.25 kg is attached at the middle of the spring and is slightly displaced along the length. The time period of the oscillation of the mass is

Moderate

A

$\frac{π}{20} s$
B

$\frac{π}{10} s$
C

$\frac{π}{5} s$
D

$\frac{π}{\sqrt{200}} s$

Solution

System is equivalent to parallel combination of springs $∴ K_{eq} = K_{1} + K_{2} = 400$ and
$T = 2 π \sqrt{\frac{m}{K_{eq}}} = 2 π \sqrt{\frac{0 .25}{400}} = \frac{π}{20}$

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