Consider the two identical simple pendulums .Discuss the their motion as a coupled oscillator and its equation
Answers
Explanation:
Two identical pendulums
We have two identical pendulums (length L) for which we consider small oscillations. In
order to find what is the simplest motion, we imagine two experiments:
1) If we draw the two masses aside some distance and release them simultaneously from
rest, they will swing in identical phase with no relative change in position. The
spring will remain unstretched (or uncompressed) and will exert no force on either
mass.
q1
q2
We call this vibration pattern the first mode of vibration of the system.
2) The other obvious way of starting a symmetric oscillation will be to stretch the spring
from both ends. If we release the masses from rest simultaneously, we may notice that:
a) The spring now exerts forces during motion
b) From symmetry of motions of A and B, their positions are mirror images of each
other
mg mg
We call this vibration pattern the second mode of vibration of the system.
Note: each pendulum in the one of the modes above oscillates with the same frequency:
the normal oscillation frequency.
The two oscillating patterns are called normal modes.
Both are SHM of constant angular frequency and amplitude.