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Thank you @haruspex and @Orodruin! I have solved the problem now.haruspex said:Your working headed off into a blind alley. You know that you need to be eliminating A, so tucking it inside an arccos function isn’t going to get you there.
Start by writing all three initial state equations: position, velocity and acceleration. Then see how you can combine them to eliminate one of the unknowns.
Thanks @haruspex! I did understand your comment, which I agree, would be very useful skill to have!haruspex said:You are welcome. But did you understand my comment about heading off into a blind alley? Recognising which directions cannot lead anywhere is a useful skill to develop.
SHM stands for Simple Harmonic Motion, which is a type of periodic motion where an object oscillates back and forth around an equilibrium point. The position function of an object in SHM describes the object's position at any given time during its motion.
The position function for an object in SHM can be derived using the equation x(t) = A*cos(ωt + φ), where A is the amplitude, ω is the angular frequency, and φ is the phase constant. This equation can be derived from the equation for displacement in SHM, x(t) = A*sin(ωt + φ), by using trigonometric identities.
The amplitude in the position function represents the maximum displacement of the object from its equilibrium point. It is a measure of the object's maximum displacement during its motion and is directly related to its energy.
The angular frequency, ω, determines the rate at which the object oscillates back and forth. A higher angular frequency results in a shorter period and a faster oscillation, while a lower angular frequency results in a longer period and a slower oscillation.
Yes, the position function can be used to determine the velocity and acceleration of an object in SHM. The velocity function, v(t), can be found by taking the derivative of the position function, and the acceleration function, a(t), can be found by taking the second derivative of the position function.