A particle moving along the x axis in simple harmonic motion starts from its equilibrium position, the origin, at t = 0 and moves to the right. The amplitude of its motion is 3.20 cm, and the frequency is 1.00 Hz. (a) Find an expression for the position of the particle as a function of time. (Use the following as necessary: t. Assume that x is in centimeters and t is in seconds. Do not include units in your answer.) (b) Determine the maximum speed of the particle. (c) Determine the earliest time (t > 0) at which the particle has this speed (d) Find the maximum positive acceleration of the particle.
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 particle moving along the x axis in
(a) Find an expression for the position of the particle as a function of time. (Use the following as necessary: t. Assume that x is in centimeters and t is in seconds. Do not include units in your answer.)
(b) Determine the maximum speed of the particle.
(c) Determine the earliest time (t > 0) at which the particle has this speed
(d) Find the maximum positive acceleration of the particle.
(e) Find the earliest time (t > 0) at which the particle has this acceleration.
(f) Determine the total distance traveled between t = 0 and t = 1.50 s.
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
