Hello i'm new to this forum and i'm facing some problems while dealing with this question.

 

A particle is moving along the x axis in SHM. It starts

from the equilibrium position and moves towards the right

at t = 0 s. The amplitude of the motion is 2 cm, and the

frequency is 1.5 Hz.

 

1)The equation for velocity can be determined by differentiating

the function for displacement w.r.t. t,

V = AWn cos (Wn t)

Therefore, the maximum speed will be

|V max| = A(Wn)(1) <---- what is this? where does the (1) come from?

 

2)The time that it first occurs

could be found as follow;

cos(Wnt) = −1, <--- why is it -1?

Wt = cos−1(−1),

t = 0.33 s.

- What is "SHM" ?

- The 1 is the maximum value that |cos(something)| can have.

- |cos(something)| = 1 implies that either cos(something)=1 or cos(something)=-1. Since I don't understand the question, I cannot tell you why it is -1. But you could probably plug in both and see which gives a smaller value for t. I'd guess that cos(something)=1 would be the case for t=0 s and therefore give the smaller time. But then, I don't really understand the question, anyways.

Ahha!!.. Thanks for the help!!!

- What is "SHM" ?

.

 

If your question is not posed as facetious (humorous), "SHM" is usually meant to be "Simple Harmonic Motion".

 

My old Calculus text says the pistons in a typical internal combustion engine move in Simple Harmonic Motion. Do you suppose that is true? imp

Yes, the question was serious. You cannot assume everyone here had his/her physics education in english and knows the common abbrevations. In fact, the use of abbrevations usually is a bad idea when there's a wide target audience.

 

Harmonic motion is the result of movement against a force F = k x, where x is the displacement from some origin and k some constant. I don't see why this should be the case for a combustion engine, but I cannot prove that it isn't the case. If your textbook sais it was the case, then it's probably a reasonably good approximation, at least. It's certainly not true for phases of acceleration (of the car) since harmonic motion implies a constant frequency which clearly isn't the case when you hit the gas pedal.