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Simple Harmonic Motion — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsSimple Harmonic Motion1 Mark
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:
  1. Remain T
  2. Become 2T
  3. Become $\frac{\text{T}}{2}$
  4. Become $\frac{\text{T}}{\sqrt{2}}$
✓

Answer

  1.  Become $\frac{\text{T}}{\sqrt{2}}$

Explanation:

Time period (T) is given by,

$\text{T}=2\pi\sqrt{\frac{\text{m}}{\text{k}}}$

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,

$\text{k}_1=2\text{k}$

New time period T1:

$\text{T}_1=2\pi\sqrt{\frac{\text{m}}{2\text{k}}}=\frac{1}{\sqrt{2}}2\pi\sqrt{\frac{\text{m}}{\text{k}}}=\frac{1}{\sqrt{2}}\text{T}$ 

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