An object's motion is described by the equation d = 4 sin(pi t ) . the displacement, d , is measured in meters. the time, t , is measured in seconds. answer the following questions:
(a) what is the object's position at t = 0 ?
(b) what is the object's maximum displacement from its resting position?
(c) how much time is required for one oscillation?
(d) what is the frequency?

Step-by-step explanation:

The given equation is:

, where d is the displacement.             (1)

(A) The position of the object at t=0 is:

⇒

⇒

The object will be at rest at t=0.

(B) In order to find the maximum displacement from the resting position, we will differentiate the given displacement.

Thus,  Differentiating with respect to t, we have

⇒

Now, d'=0

⇒

⇒

⇒

⇒

Substitute the value of t in equation (1), we get

⇒

⇒

⇒

Thus, the maximum displacement from its resting position will be 4m.

(C) Time required for one oscillation is equal to the period which is equal to=

thus,  time  required for one oscillation will be 2 seconds.

(D) Frequency is nothing but the reciprocal of period that is

Thus, the frequency will be equal to .

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step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

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step-by-step explanation: