Question

A spring with no mass attached to it hangs from a rigid support. A mass m is now hung on the lower end to the spring. The mass is supported on a platform so that the spring remains relaxed. The supporting platform is then suddenly removed and the mass begins to oscillate. The lowest position of mass during the oscillation is 5 cm below the place where it was resting on the platform. What is the angular frequency of oscillation? Take $g=10m{s}^{-2}$

• A. $10rad{s}^{-1}$
• B. $20rad{s}^{-1}$
• C. $30rad{s}^{-1}$
• D. $40rad{s}^{-1}$

Answer 1

Answer: (B)

$20rad{s}^{-1}$

$\omega =2\pi n=2\pi \sqrt{\frac{K}{m}}$

$a=5cm$

$g=10cm$

$v=a\omega$

$\omega =\frac{v}{a}$ $\Rightarrow \omega =\sqrt{\frac{K}{m}}=\sqrt{2gL}$

$\omega =\sqrt{2\times 10\times 10}=20rad/s$