A mass of 0.38 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by x(t) = (0.26 m)cos[(16 rad/s)t]. Determine the following. %3D (a) amplitude of oscillation for the oscillating mass How does the amplitude of oscillation compare to the magnitude of the maximum displacement from equilibrium? m (b) force constant for the spring N/m (c) position of the mass after it has been oscillating for one half a period m (d) position of the mass one-third of a period after it has been released (e) time it takes the mass to get to the position x = -0.10 m after it has been released
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 mass of 0.38 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass
is described by x(t) = (0.26 m)cos[(16 rad/s)t]. Determine the following.
%3D
(a) amplitude of oscillation for the oscillating mass
How does the amplitude of oscillation compare to the magnitude of the maximum displacement from equilibrium? m
(b) force constant for the spring
N/m
(c) position of the mass after it has been oscillating for one half a period
m
(d) position of the mass one-third of a period after it has been released
(e) time it takes the mass to get to the position x = -0.10 m after it has been released](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f619dbb-fdef-460b-b92d-9112a1596c50%2Fc1f448bc-0867-495c-ab68-08b52c333717%2Fma8p5s7_processed.png&w=3840&q=75)
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