Question

A spring with no mass attached to it hangs from 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

Hint:In this type of problem, we should be aware of the different types of formula used here. How the different values of the variable of the formula is used from the question. The frequency oscillation formula is modified and used here to take out the required solution for the problem given here. Calculate wavelength. Solve using given data.

Complete step-by-step answer:
We know that t find frequency oscillation calculate wavelength
$w=2\pi n$
Put value for N.
$w=2\pi \sqrt{\dfrac{K}{m}}$
Given,
The lowest position of mass during the oscillation is $a=5cm$
$g=10cm$
The mass is supported on a platform so that the spring remain relaxed
$v=aw$
Can also be written as,
$w=\dfrac{v}{a}$
Also,
$w=\sqrt{\dfrac{K}{m}}=\sqrt{2gL}$
Putting values we get,
$w=\sqrt{2\times 10\times 10}=20rad/s$
Therefore the final answer is $20rad/s$

Note:While solving this question, we should be aware of the different types of formula used here. Especially w and how the different values of the variable of the formula is used from the question. The finding w formula is modified and used here to take out the required solution for the problem given here.