First slide

Simple harmonic motion

Question

When a particle is performing linear SHM its KE is two times its PE at a position ‘A’ and its PE is two times its KE at another position ‘B’. Find ratio of ${KE}_{A}$ to ${KE}_{B}$

Moderate

A

$\frac{3}{2}$
B

$\frac{2}{1}$
C

$\frac{3}{4}$
D

$\frac{5}{2}$

Solution

$A t A, K E = 2 P E, \Rightarrow P E = K E / 2, T E = K E + P E, s u b s t i t u t e, T E = K E + \frac{K E}{2}, \Rightarrow T E_{A} = \frac{3 K E_{A}}{2} - - - (1) A t B, P E = 2 K E, T E = K E + P E, s u b s t i t u t e, T E = K E + 2 K E, \Rightarrow T E_{B} = 3 K E_{B} - - - - (2) a c c o r d i n g t o p r i n c i p l e o f c o n s e r v a t i o n o f e n e r g y T E_{A} = T E_{B} \frac{3 K E_{A}}{2} = 3 K E_{B} \Rightarrow \frac{K E_{A}}{K E_{B}} = \frac{2}{1}$

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