First slide

Applications of SHM

Question

When a body of mass 1.0 kg is suspended from a certain light spring hanging vertically, its length increases by 5 cm. By suspending 2.0 kg block to the spring and if the block is pulled through 10 cm and released the maximum velocity in it in m/s is : (Acceleration due to gravity $= 10 m / s^{2})$

Moderate

A

0.5
B

1
C

2
D

4

Solution

Initially when 1 kg mass is suspended then by using $F = kx \Rightarrow mg = kx \Rightarrow k = \frac{mg}{x} = \frac{1 \times 10}{5 \times 10^{- 2}} = 200 \frac{N}{m}$
Further, the angular frequency of oscillation of 2 kg mass is $ω = \sqrt{\frac{k}{M}} = \sqrt{\frac{200}{2}} = 10 rad / \sec$
Hence, $v_{\max} = aω = (10 \times 10^{- 2}) \times 10 = 1 m / s$

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