Determine the magnitude of the force, in newtons, required to initially displace the sphere d=12�=12 centimeters from equilibrium. b. What is the sphere's distance from equilibrium, in meters, at time t=1�=1 second? c. Determine the frequency, in hertz, with which the spring–mass system oscillates after being released. d. Calculate the maximum speed, in meters per second, attained by the sphere. e. At what point in the motion does the sphere reach maximum speed? f. Calculate the magnitude of the maximum acceleration, in meters
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 sphere of mass m=3.5 kg can move across a horizontal, frictionless surface. Attached to the sphere is an ideal spring with spring constant k=24 N/m. At time t=0the sphere is pulled aside from the equilibrium position, x=0, a distance d=12 cm in the positive direction and released from rest. After this time, the system oscillates between x=±d.
a. Determine the magnitude of the force, in newtons, required to initially displace the sphere d=12�=12 centimeters from equilibrium.
b. What is the sphere's distance from equilibrium, in meters, at time t=1�=1 second?
c. Determine the frequency, in hertz, with which the spring–mass system oscillates after being released.
d. Calculate the maximum speed, in meters per second, attained by the sphere.
e. At what point in the motion does the sphere reach maximum speed?
f. Calculate the magnitude of the maximum acceleration, in meters per second squared, experienced by the sphere.
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