Am self studying SHM, so sorry for the elementary questions.
Would someone check/confirm some facts i think I've learned please.
1 If a sine wave graph starts at the origin at time = 0s, the sysyem is in equilibrium?
2 The amplitude at t= 0s is zero.
3 Same system, the phase angle/constant (phi) is 0 or pi?
4 When a system is displaced, but at rest, the phase angle is + or - half pi?
Confirmation or advice appreciated
Thanks
1. What does the sine wave represent?
2. Yes. If your sine wave is amplitude.
3. This makes no sense.
4. yes.
Sorry Bob,
The wave represents a simple pendulum.
In 3, I'm referring to the equation
x(t)=Asin(wt+(greek letter phi)), so was looking to confirm that in that specific circumstance I outlined, the value of phi would either be zero or pi (as in 22/7).
Thanks.
No problem! I can help you confirm your understanding of Simple Harmonic Motion (SHM).
1. If a sine wave graph starts at the origin (zero position) at time t = 0s, then the system is indeed in equilibrium. In SHM, equilibrium refers to the position where the net force acting on the system is zero.
2. Yes, in SHM, if the system is at the equilibrium position at t = 0s, the amplitude (maximum displacement from equilibrium) would be zero at that particular instant.
3. The phase angle (denoted by the Greek letter phi, φ) depends on the initial conditions of the system. If the system starts at the origin (equilibrium) and moves in the positive direction, then the phase angle φ would be zero. On the other hand, if the system starts at the origin and moves in the negative direction, then the phase angle φ would be pi (180 degrees).
4. When a system is displaced from its equilibrium position but at rest (not in motion), the phase angle φ would be either +π/2 (90 degrees) or -π/2 (-90 degrees), depending on the direction of the displacement.
To confirm your answers, it's always a good idea to consult your study materials or check with your teacher or tutor if you have any doubts. Remember, the key to mastering SHM is practice and understanding the underlying principles. Keep up the good work!