Two pendulums with identical bobs and lengths are suspended from … - Vidyadip

Question

Two pendulums with identical bobs and lengths are suspended from a common support such that in rest position the two bobs are in contact. One of the bobs is released after being displaced by 10° so that it collides elastically head-on with the other bob.

Describe the motion of two bobs.
Draw a graph showing variation in energy of either pendulum with time, for where T is the period of each pendulum.

✓

Answer

Let at t = 0 A is at lowest position and B is at its height position at 10°

PE_A = 0, PE_B = E, KE_A = KE_B = 0

K.E. of both are zero. Now bob is released.

Click and drag to move reaches to A and collide elastically as both bobs are identical then,

KE_A = 0, KE_B = E, PE_A = 0

PE_B = 0

AT Click and drag to move reaches at it’s maximum height and B remains at it’s lowest position.

KE_A = 0, KE_B = E, PE_A = E, PE_B = 0

At Click and drag to move Bob A hits the bob B which was at rest elastically and ball A becomes at rest, B moves upward.

KE_A = 0, KE_B = E, PE_A = E, PE_B = 0

E_A = 0, E_B = E

At Click and drag to move Bob B is at its maximum height and A is at lower height.

So, KE_A = 0, KE_B = 0, PE_A = 0, PE_B = E

The entire process is repeated.

Time t	KE_A	PE_A	E_A	KE_B	PE_B	E_B
0	0	0	0	0	E	E
	0	0	E	0	0	0
	0	0	0	0	E	E
	E	0	E	0	0	0
	0	0	0	0	E	E

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