Two pendulums are attached to a massless spring, as shown above. The arms of the pendulums are of identical lengths l, but the pendulum balls have unequal masses m1 and m2. The initial distance between the masses is the equilibrium length of the spring, which has spring contant K. What is the highest normal mode frequency of this system?
A.
B.
C.
D.
E.
(GR9677 #84)
A. FALSE
ω = √(g/l) is angular frequency for single pendulum
B. and C are FALSE
Both answers do not depend on g/l
D. TRUE
If there is no dependence on K → ω = √(g/l)
And if m2 → ∞, m1 will still oscillate with spring constant K but has no dependence on m2, as if it were connected to a stationary object.
E. FALSE
If there is no dependence on K → ω = √(2g/l), not angular frequency for single pendulum
And if m2 → ∞, ω = √(2g/l) has no dependence on K and m1
Answer: D
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