A 2kg mass is attached to a spring and placed on a horizontal, smooth surface. A horizontal force of 20N is required to hold the mass at rest when it is pulled 0.2 m from its equilibrium position (the origin of the x axis). The mass is now released form rest with an initial displacement of x1= 0.2 m, and it subsequently undergoes simple harmonic oscillations. a) Find the force constant of the spring. b) Find the frequency of the oscillations. c) Find the maximum speed of the mass. Where does this maximum speed occur? d) Find the maximum acceleration of the mass. Where does this maximum speed occur? e) Find the total energy of the oscillating system. f) Find the speed when the displacement equals one third of the maximum value. g) Find the acceleration when the displacement equals one third of the maximum value.
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 2kg mass is attached to a spring and placed on a horizontal, smooth surface. A horizontal force of 20N is required to hold the mass at rest when it is pulled 0.2 m from its equilibrium position (the origin of the x axis). The mass is now released form rest with an initial displacement of x1= 0.2 m, and it subsequently undergoes simple harmonic oscillations.
a) Find the force constant of the spring.
b) Find the frequency of the oscillations.
c) Find the maximum speed of the mass. Where does this maximum speed occur?
d) Find the maximum acceleration of the mass. Where does this maximum speed occur?
e) Find the total energy of the oscillating system.
f) Find the speed when the displacement equals one third of the maximum value.
g) Find the acceleration when the displacement equals one third of the maximum value.
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