A simple pendulum, which has been given a small displacement, will perform simple harmonic motion. The time period T of the resulting oscillations is given by T = 2π p l/g, where l is the length of the pendulum and g is the gravitational field strength (g = 9.8 m s−2 ). Consider two pendulums with lengths l1 and l2. Express their periods T1 and T2 in terms of l1 and l2. Find the ratio l1/l2, if it is given that the first pendulum swings back and forth 10 times per minute, while the second one swings back and forth 300 times per hour.
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.
A simple pendulum, which has been given a small displacement, will perform
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