First slide

Periodic Motion

Question

A simple pendulum of length / is vibrating with an amplitude A.Its energy is E. Consider the following situations:
(i) Amplitude is doubled keeping length the same
(ii) Length is doubled, keeping amplitude the same.
Then energy of the pendulum in the two situations will be:

Moderate

A

$4 E, \frac{E}{2}$
B

$2 E, \frac{E}{2}$
C

E,E
D

2E,2E

Solution

$E = \frac{1}{2} {mω}^{2} A^{2}$
(i) $A' = 2 A \Rightarrow E' = 4 E$
(ii) $T \propto \sqrt{l} \Rightarrow T' = \sqrt{2} T, E' \propto ω^{2} \propto \frac{1}{T^{2}} \Rightarrow E' = \frac{E}{2}$

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