Hi Im confuse the question C, can you explan why should use cos-1 instead of sin

Question

Hi Im confuse the question C, can you explan why should use cos-1 instead of sin? and can you tell me when we should use Y=Ymsin(kx+wt)?

40 marks spend about 60 minutes on this section QUESTION B1 (1 l 1 1 2 2 8 marks) The end of one of the prongs of a tuning fork that executes simple harmonic motion of frequency 1000 Hz has amplitude of 0.40 mm a) Find the magnitude of the maximum acceleration of the end of the prong. A-a x (2 (1000 Hz)) (0.40x10-am -16x10 m/s b) What is the maximum speed of the end of the prong? V -2 (1000 Hz) (0.40x10- m)-2.5m/s. c) What is the phase of the motion of the end of the prong, when the end has a displacement of 0.20 mm?

Explanation / Answer

First,

If at t = 0, x = 0 then we can use sin and take = 0 degree, as x = X sin (wt + ) = X sin (w*0 + 0) = X sin (0) = 0.

At the same time, if we want to use cos then we have to take = 90 degree as x = X cos (wt + ) = X cos (w*0 + 900) = X cos (900) = 0.

Second

As here we are concerned with the motion of end of prong which changes its position with time as per

x = X cos (wt + ) which tells us that at a specific time there will be a particular value of x. So here we can’t use y = Ym cos (wt + kx) in spite of x = X cos (wt + ) because y = Ym cos (wt + kx) represents a travelling wave for which a quantity varies with time as well as with position. The biggest difference here is that for end of prong, it is its position which changes with time while for a wave it is some quantity which changes with time as well as position. So we will use y = Ym cos (wt + kx) for a travelling wave for which some quantity changes with time as well as with position.

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