An object with mass m is attached to a spring with stiffness k. The mass is oscillating on a smooth horizontal surface. The position as a function of time graph of the motion is shown here. 0.20 0.10 0.5 1 1.5 2 2.5 -0.10 -0.20 t [s] a) Find the amplitude of the motion and the period of the motion using the graph. b) Write the equations for position and velocity. (Including numbers). c) Show the first four places on this graph where the velocity of the oscillator is zero. Explain your reasoning. 3. [u] (1)x
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 with mass m is attached to a spring with stiffness k. The mass is oscillating on a
smooth horizontal surface. The position as a function of time graph of the motion is shown
here.
0.20
0.10
0.5
1
1.5
2
2.5
3
-0.10
-0.20
t [s]
a) Find the amplitude of the motion and the period of the motion using the graph.
b) Write the equations for position and velocity. (Including numbers).
c) Show the first four places on this graph where the velocity of the oscillator is zero.
Explain your reasoning.
d) Use the equations to find the first four times when the velocity is zero. Compare
these times against the places you indicated in your graph in (c). Comment on the
agreement.
e) Use the attached graph paper (or use your own with the same scale) and draw the
velocity vs time graph for this oscillator. Make sure you indicate the maximum
velocity and its value. Plot accurately.
1.6
0.8 +
+
+
t [s]
0.5
1.0
1.5
2.0
-0.8
-1.6
[u] (1)x
[s/w] (1)a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5910d2b7-72c3-411e-9760-e0829938261b%2F0a42f52c-d0b7-4d05-bc84-b2ccadf7587e%2Fwhyseus_processed.png&w=3840&q=75)
Oscillation is the back and forth motion of a particle in regular interval of time.
Amplitude of a wave is the maximum displacement of the wave.
Time period of a oscillation is the time taken for one complete oscillation.
Angular frequency is given by,
(1)
Velocity is the derivative of position with respect to time.
Velocity is given by,
(2)
Where,
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