Question 3 Two objects of equal mass on an effectively frictionless horizontal air track are held between rigid supports by three identical springs, as shown in the figure below. The displacements from equilibrium along the line of the springs are described by coordinates xA and xB. If either of the masses is clamped, the period T for one complete vibration of the other is 3 sec. lellll ell (a) write out the equations of motion for the system. (b) If both objects are free, what are the periods of the two nomal modes of the system? At t = 0, mass A is at its normal resting position and object B is pulled aside a distance of 5 cm. The masses are released from rest at this instant. (c) write an equation for the subsequent displacement of each object as a function of time. (d) What is the time (in seconds) characterises the periodic transfer of the motion from B to A and back again?
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
Coupled oscillations question
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