First slide

Simple hormonic motion

Question

A body executes sample harmonic motion under the action of a force $F_{1}$ with a time period (4/5) sec. If the force is changes to $F_{2}$ it executes SHM with time period (3/5) sec. if both the forces $F_{1} a n d F_{2}$ act simultaneously in the same direction on the body, its time period (in seconds) is:

Moderate

A

12/25
B

24/25
C

35/24
D

25/12

Solution

$\begin{array}{l} o r k = k_{1} + k_{2} \\ o r m ω^{2} = m ω_{1}^{2} + m ω_{2}^{2} \\ o r ω^{2} = ω_{1}^{2} + ω_{2}^{2} \end{array}$
$\begin{array}{l} ∴ T = \frac{T_{1} T_{2}}{\sqrt{T_{1}^{2} + T_{2}^{2}}} \\ = \frac{\frac{4}{5} \times \frac{3}{5}}{\sqrt{{(\frac{4}{5})}^{2} + {(\frac{3}{5})}^{2}}} = \frac{12}{25} \sec \end{array}$

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