Q1: When we measure the acceleration of gravity g, why is it important to keep the
amplitude of the swinging pendulum small?

Q2: What condition or conditions are required for simple harmonic motion to occur?

Q3: Suppose you have a simple pendulum consisting of a mass m at the end of a massless
string of length L. What would happen to the period T of the pendulum if you doubled the
mass m?

Question

Answered

Sagot :

Upendoid Upendoid · Answer 1

1. This is sorely to reduce error as larger amplitude will increase angle of deflection thus creating much space for blunders.

2. Conditions;

* The object must exhibit periodic motion that is to and fro motion about it's mean position.

* The restoring force must be directly proportional to the extension and must act opposite the direction of the motion.

* The acceleration must be directly proportional to the extension and act opposite the direction about the mean position.

3. It's known,

[tex]t = 2\pi \sqrt{ \frac{m}{k} } [/tex]

from 1st eqn, when mass is doubled then m will be 2m

and,

[tex] {t }^{2} = 4 {\pi}^{2} ( \frac{m}{k} )[/tex]

thus, 2m will increase T by factor of √2.