Question

A small marble attached to a massless thread is hung from a horizontal support. When the marble is pulled back a small distance from equilibrium and released, it swings in simple harmonic motion with a frequency ????f.
What is the frequency of the pendulum if the length of the thread is increased by a factor of 4,4, but the marble is still released in the same way?
a,4????4f
b.2????2f
c.????f
d.????2f2
e.????4

Answer 1

Answer:

f' = 2 f

Explanation:

The frequency of the pendulum that swings in simple harmonic motion is given by :

$f={2\pi}\sqrt{\dfrac{l}{g}}$

Where

l is the length of pendulum

g is the acceleration due to gravity

If the length of the thread is increased by a factor of 4, such that, l' = 4 l, let f' is the new frequency such that,

$f'={2\pi}\sqrt{\dfrac{l' }{g}}$

$f'={2\pi}\sqrt{\dfrac{4l}{g}}$

$f'=2\times {2\pi}\sqrt{\dfrac{l}{g}}$

f' = 2 f

So, the new frequency of the pendulum will become 2 time of initial frequency. Hence, the correct option is (b) "2f"