First slide

Simple hormonic motion

Question

When a block A is suspended by a spring and allowed to oscillate vertically, its time period of oscillation is found to be 3 sec. When another block B is suspended by the same spring, its time period of oscillation is found to be 4 sec. Now the two blocks A and B are tied together, suspended by the same spring and allowed to oscillate vertically. Then time period of the composite block is

Moderate

A

7 sec
B

8 sec
C

5 sec
D

3.5 sec

Solution

For a spring-mass system, $T = 2 π \sqrt{\frac{m}{K}} \Rightarrow m = \frac{{KT}^{2}}{4 π^{2}}$
$∴ \frac{{KT}^{2}}{4 π^{2}} = \frac{{KT}_{1}^{2}}{4 π^{2}} + \frac{{KT}_{2}^{2}}{4 π^{2}}$
$\Rightarrow T = \sqrt{T_{1}^{2} + T_{2}^{2}} = \sqrt{3^{2} + 4^{2}} \sec = 5 \sec$

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