Question

An object of unknown mass m is hung from a vertical spring of unknown spring constant k, and the object is observed to be at rest when the spring has stretched by 17 cm .
The object is then given a slight push upward and executes SHM Part A Determine the period T of this oscillation.
Express your answer to two significant figures and include the appropriate units.

Answer 1

Explanation:

It is given that,

Let m is the mass of the object that is hung from a vertical spring of unknown spring constant k. When the spring is stretched by 17 cm, the object executes SHM. Let T is the period of oscillation that is given by :

$T=2\pi \sqrt{\dfrac{m}{k}}$.............(1)

The gravitational force is balanced by the force of spring at equilibrium as :

$mg=kx$

$\dfrac{m}{k}=\dfrac{x}{g}$

So, equation (1) becomes :

$T=2\pi \sqrt{\dfrac{x}{g}}$

x = 17 cm = 0.17 m

$T=2\pi \sqrt{\dfrac{0.17\ m}{9.8\ m/s^2}}$

T = 0.82 seconds

So, the period of this oscillation is 0.82 seconds. Hence, this is the required solution.