A particle moves along the x axis. It is initially at the position 0.260 m, moving with velocity 0.050 m/s and acceleration -0.400 m/s2. Suppose it moves with constant acceleration for 3.70 s. We take the same particle and give it the same initial conditions as before. Instead of having a constant acceleration, it oscillates in simple harmonic motion for 3.70 s around the equilibrium position x = 0. Hint: the following problems are very sensitive to rounding, and you should keep all digits in your calculator. The angular frequency is 1.24/s. Amplitude of oscillation is 0.2631m. (e) Find its phase constant ϕ0 if cosine is used for the equation of motion. Hint: when taking the inverse of a trig function, there are always two angles but your calculator will tell you only one and you must decide which of the two angles you need. (f) Find its position after it oscillates for 3.70 s. (g) Find its velocity at the end of this 3.70 s time interval.
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.
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A particle moves along the x axis. It is initially at the position 0.260 m, moving with velocity 0.050 m/s and acceleration -0.400 m/s2. Suppose it moves with constant acceleration for 3.70 s.
We take the same particle and give it the same initial conditions as before. Instead of having a constant acceleration, it oscillates in
The angular frequency is 1.24/s.
Amplitude of oscillation is 0.2631m.
(e) Find its phase constant ϕ0 if cosine is used for the equation of motion. Hint: when taking the inverse of a trig function, there are always two angles but your calculator will tell you only one and you must decide which of the two angles you need.
(f) Find its position after it oscillates for 3.70 s.
(g) Find its velocity at the end of this 3.70 s time interval.
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