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.
The simple pendulum is a mechanical device that illustrates several concepts about forces and motion. The simple pendulum uses a string or cord to suspend a mass at some length from a pivot point. The mass is called the bob and when displaced from rest, will move in
The last thing this experiment will show is that the relationship between the length of the pendulum and the pendulum’s period (the time for one cycle) can be described by the statement: the period of a pendulum is directly proportional to the square root of the length of the pendulum. Or that the length of the pendulum is directly proportional to the square of the pendulum’s period. Three different lengths of string will be used to measure the period of the pendulum and a graph will be made of the period’s time squared and the length.
MECHANICS OF A SIMPLE PENDULUM Any simple pendulum can be described by the relationship between the pendulum’s period of oscillation, the length of the pendulum, and the gravitational acceleration. This relationship is given by the equation where T is the time in seconds for one cycle, L is the length of the pendulum from the pivot point to the center of mass of the bob, and g is the acceleration from gravity. Notice that there is no mass variable in this equation, meaning that mass has no effect on the motion of a pendulum. We can measure the period of the pendulum with a stopwatch, we can also measure the length of the pendulum. If we then solve the equation for g, we can determine the gravitational acceleration using a simple pendulum. Taking the equation above we can divide both sides of the equation by 2π which then gives, we can then square both sides of the equation to get rid of the radical, which gives us, we can then use the reciprocal rule to invert both sides of the equation which gives, finally we multiply both sides of the equation by L to isolate g by itself, which gives us, We will use this equation to determine g from the pendulum’s period and length.
3. A simple pendulum has a length of 30 cm. What is the pendulum’s period? Show your calculation.
4. When timing the period of the pendulum in the lab, why does timing ten cycles of the pendulum provide better accuracy than timing one cycle of the pendulum ten times?
5. Based on Newton’s Second Law, why does the mass of the suspended bob apparently have no effect on the period of a pendulum’s motion? Explain.
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