A 2.0-kg cart attached to a spring undergoes simple harmonic motion on a low-friction surface. Its displacement-versus-time is described by: 27 (0.20m) cos 2.0s This is the same situation you’ve worked with in Activities 2.5 and 4.2 Work with your group to figure out the following: a. Determine the period and the amplitude of the motion. b. Determine the spring constant of the spring to which the cart is attached. c. Determine the maximum elastic potential energy of the system.
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 2.0-kg cart attached to a spring undergoes simple harmonic motion on a low-friction surface.
Its displacement-versus-time is described by:
[()]
27
(0.20m) cos
2.0s
This is the same situation you’ve worked with in Activities 2.5 and 4.2
Work with your group to figure out the following:
a. Determine the period and the amplitude of the motion.
b. Determine the spring constant of the spring to which the cart is attached.
c. Determine the maximum elastic potential energy of the system.
d. Determine the maximum speed of the cart. At what position(s) does this maximum v occur?
e. Write a general mathematical expression for the velocity as a function of time using the given
numbers.
f. Determine the maximum acceleration of the cart. At what position(s) does this maximum a
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