A glider moves in simple harmonic motion on a horizontal, frictionless track by connecting it to a spring of stiffness 250 N/m. The phone accelerometer detected the motion of the glider by recording its acceleration as a function of time, as shown in the figure below ax (m/s²) 12.0 6.0 O -6.0 -12.0 t(s) 0.10 0.20 0.30 0.40 From the graph [note: this is an acceleration vs. time plot], compute for the following quantities: a. the period T, b. the frequency f c. the angular frequency ;
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 glider moves in simple harmonic motion on a horizontal, frictionless track by connecting it to a spring of
stiffness 250 N/m. The phone accelerometer detected the motion of the glider by recording its acceleration
as a function of time, as shown in the figure below
a, (m/s²)
12.0
6.0
0
-6.0
-12.0
A
0/10 0.20 0.30 0.40
t(s)
From the graph [note: this is an acceleration vs. time plot], compute for the following quantities:
a. the period T;
b. the frequency f
c. the angular frequency ;
d. the mass of the glider, m;
e. the maximum force experienced by the glider, Fax:
f. the amplitude of oscillation, A;
g. the starting position xo:
h. the phase angle ;
i. the expression for the position vs. time, x(t);
j.
the expression for the velocity vs. time, v(t);](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F587cc756-39aa-41e2-b8c5-d7793c8508b4%2F29c59d36-716e-4351-bdbe-eee5b9356f7a%2Fa5xqe9q_processed.jpeg&w=3840&q=75)
Step by step
Solved in 3 steps with 1 images
