1. A 0.5 kg mass is attached vertically on the spring and stretches 0.3 m. The set-up the spring horizontally on a frictionless table with the same mass. The mass is pushed so that the spring will be compressed at 0.15 m and released. Assume simple harmonic motion. a. Calculate the spring constant (k) and angular frequency (angular frequency, w = 2Tf ). b. Calculate the maximum acceleration and velocity c. Calculate the frequency (Hz) and period of vibration (seconds). (For spring-mass systems, use T = 2n k is in N/m] where m is in kg and
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.
![Solve the following problem, create a simple illustration, and
show your solutions.
1. A 0.5 kg mass is attached vertically on the spring and stretches
0.3 m. The set-up the spring horizontally on a frictionless table with
the same mass. The mass is pushed so that the spring will be
compressed at 0.15 m and released. Assume simple harmonic
motion.
a. Calculate the spring constant (k) and angular frequency (angular
frequency, w = 2f ).
b. Calculate the maximum acceleration and velocity
c. Calculate the frequency (Hz) and period of vibration (seconds).
[For spring-mass systems, use T = 2n
k is in N/m]
where m is in kg and](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd7cede84-2c30-4e15-81f2-7c4882defddb%2F2187ad30-ff95-4386-a9d6-e29c6a030bfe%2Feg0p19_processed.png&w=3840&q=75)
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