**Answer:**

**(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**