Classical Mechanics - Simple Harmonic Oscillation

Three masses are connected by two springs as above. A longitudinal normal mode with frequency ¹/_2π√^k/_m is exhibited by

1. A, B, C all moving in the same direction with equal amplitude.
2. A and C moving in opposite, and B at rest.
3. A and C moving in the same direction with equal amplitude, and B moving in the opposite direction with the same amplitude.
4. A and C moving in the same direction with equal amplitude, and B moving in the opposite direction with twice the amplitude.
5. None of the above.

(GR8677 #43)

Solution:

Angular frequency, ω = 2πf  → f = ^ω/_2π
For Simple Harmonic Oscillation (SHO), ω = √^k/_m
Thus, f = ¹/_2π√^k/_m is frequency of SHO.

SHO is a periodic motion of a particle about a fixed point (the centre of motion).

Only choice (B) gives a fixed point (mass B at rest).

Answer: B