First slide

Applications of SHM

Question

A body at the end of a spring executes SHM with a period t₁, while the corresponding period for another spring is t₂. If the period of oscillation with the two spring in series is T, then

Moderate

A

$T = t_{1} + t_{2}$
B

$T^{2} = t_{1}^{2} + t_{2}^{2}$
C

$\frac{1}{T} = \frac{1}{t_{1}} + \frac{1}{t_{2}}$
D

$\frac{1}{T^{2}} = \frac{1}{t_{1}^{2}} + \frac{1}{t_{2}^{2}}$

Solution

$\begin{array}{l} T_{1} = 2 π \sqrt{\frac{m}{k_{1}}}, T_{2} = 2 π \sqrt{\frac{m}{k_{2}}}, T = 2 π \sqrt{\frac{m}{k_{eq}}} \\ k_{eq} = \frac{k_{1} k_{2}}{k_{1} + k_{2}} (for series), t_{1}^{2} = \frac{2 π m}{k_{1}} \\ t_{2}^{2} = \frac{2 π m}{k_{2}} and T^{2} = 2 π m (\frac{1}{k_{1}} + \frac{1}{k_{2}}) \\ \Rightarrow T^{2} = t_{1}^{2} + t_{2}^{2} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App