The weight of an empty railway vehicle is 220 kN. On loading it with goods weighing 370 kN, its spring gets compressed by 28 cm. (a) Calculate its natural period of vibrations when the vehicle is (i) empty and (ii) loaded as above. (b) It is set into natural vibrations with an amplitude of 280 mm when loaded. Calculate the velocity and acceleration of the vehicle when its displacement is 70 mm from statically equilibrium position. Also calculate the maximum acceleration
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.
Step by step
Solved in 3 steps
