An object oscillates up and down between y = +A and y= −A at the end of a stretched At what point(s) is the total potential energy (gravitational + elastic) minimum ? At what point(s) is the elastic potential energy maximum? At what point(s) is the elastic potential energy maximum? y= +A y= -A Y= 0 y= +A or Y= -A
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.
An object oscillates up and down between y = +A and y= −A at the end of a stretched
At what point(s) is the total potential energy (gravitational + elastic) minimum ?
At what point(s) is the elastic potential energy maximum?
At what point(s) is the elastic potential energy maximum?
y= +A
y= -A
Y= 0
y= +A or Y= -A
At the end of a stretched, it is a given that an object oscillates up and down between y = +A and y=-A.
It is required to find the points:
- where the total potential energy (gravitational + elastic) minimum
- where the elastic potential energy maximum
It is known that, the gravitational potential energy is calculated as:
Here m is the mass of the object, g is the acceleration due to gravity, and h is the height from the system's bottom point.
and the elastic potential energy is calculated as:
Here k is the spring constant, and y is the length stretched or compressed by the body.
Therefore, the total potential energy is:
We can express this problem with the following diagram:
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