A force of 2 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force that is numerically equal to 0.4 times the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position. b) Express the equation of motion (c) Find the rst time at which the mass passes through the equilibrium position heading upward.
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.
29. A force of 2 pounds stretches a spring 1 foot. A mass weighing
3.2 pounds is attached to the spring, and the system is then
immersed in a medium that offers a damping force that is
numerically equal to 0.4 times the instantaneous velocity.
(a) Find the equation of motion if the mass is initially released
from rest from a point 1 foot above the equilibrium position.
b) Express the equation of motion
(c) Find the rst time at which the mass passes through the
equilibrium position heading upward.
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