First slide

Simple hormonic motion

Question

Frequency of oscillation of a block with two springs separately are 3Hz and 4Hz. Frequency of oscillation of same block with both springs connected in parallel is

Moderate

A

7 Hz
B

5 Hz
C

$\frac{12}{7}$ Hz
D

10 Hz

Solution

$f = \frac{1}{2 π} \sqrt{\frac{k}{m}}; 3 = \frac{1}{2 π} \sqrt{\frac{k_{1}}{m}} \Rightarrow \frac{k_{1}}{m} = (6 π)^{2} & 4 = \frac{1}{2 π} \sqrt{\frac{k_{2}}{m}} \Rightarrow \frac{k_{2}}{m} = (8 π)^{2} f = \frac{1}{2 π} \sqrt{\frac{k_{1} + k_{2}}{m}} \Rightarrow f = \frac{1}{2 π} \sqrt{(6 π)^{2} + (8 π)^{2}} = 5 Hz$

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