Question

A particle executes simple harmonic motion under the restoring force provided by a spring. The time period is T. If the spring is divided in two equal parts and one part is used to continue the simple harmonic motion, the time period will

Options

• remain T

• become 2T

• become T/2

• become \[T/\sqrt{2}\]

Answer 1

become \[T/\sqrt{2}\]

Time period \[\left( T \right)\] is given by,

\[T = 2\pi\sqrt{\frac{m}{k}}\]

where m is the mass, and
          k is spring constant.

When the spring is divided into two parts, the new spring constant k₁ is given as,
k₁ =\[2k\]

New time period T₁ :
T₁  = \[2\pi\sqrt{\frac{m}{2k}} = \frac{1}{\sqrt{2}}2\pi\sqrt{\frac{m}{k}} = \frac{1}{\sqrt{2}}T\]