The function x = (5.2 m) cos[(5πrad/s)t + π/5 rad] gives the simple harmonic motion of a body. At t = 5.3 s, what are the (a) displacement, (b) velocity, (c) acceleration, and (d) phase of the motion? Also, what are the (e) frequency and (f) period of the motion?

(a) Displacement = - 3.0576 m

(b) Velocity   m/s

(c)Acceleration   = -753.39 m²/s

(d)The phase motion is 26.7 .

(e)Frequency =2.5 Hz.

(f)Time period =0.4 s

Explanation:

Given function is

(a)

The displacement includes the parameter t, so,at time t=5.3 s

           =(5.2)(-0.588)m

           = - 3.0576 m

(b)

To find the velocity of simple harmonic motion, we need to find out the first order derivative of the function.

Now we can plug our value t=5.3 into the above equation

  m/s

(c)

To find the acceleration of simple harmonic motion, we need to find out the second order derivative of the function.

Now we can plug our value t=5.3 into the above equation

  = -753.39 m²/s

(d)

The general equation of SHM is

is amplitude of the displacement, is phase of motion, is phase constant.

So,

Now plugging t=5.3s

             =26.7

The phase motion is 26.7 .

The angular frequency

(e)

The relation between angular frequency and frequency is

   = 2.5 Hz

Frequency =2.5 Hz.

(f)

The relation between frequency and time period is

  =0.4 s

Time period =0.4 s

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