**Problem one and solution**

Find the average speed and
average velocity of a particle after completion of one oscillation?

While solving this problem we can
understand one simple point that average velocity is the ratio of total
displacement to the total time. When the body completes one complete
oscillation it comes back to its original position and hence its displacement
is equal to

**0**therefore its average velocity is also equal to**0**.
Anyway while we are calculating
the average as speed it is defined as the ratio of the total distance traveled to
the total time taken for the journey. In the process of completing one
oscillation the body completes a distance
equal to 4 times of its amplitude. Therefore it will have a certain
speed as shown below.

**Problem Two and solution**

Find the displacement of a body in simple harmonic motion at which the magnitude of the acceleration is
equal to the magnitude of velocity?

Solving this problem shall be a
simple task once if you know the equations that we have derided for velocity
and acceleration. This is just substituting the numerical values of the velocity
and acceleration we can get the answer as shown below.

**Prob**

**lem three and solution**

Find the displacement of a
particle simple harmonic motion where velocity of the vertically is half of its
maximum velocity ?

This problem also can be solved
basing on the mathematical equations that we had derived for the velocity and
acceleration of a body in simple harmonic motion as shown below.

**Problem four and solution**

A graph is drawn between
acceleration the displacement of a body who is an simple harmonic motion.
The graph is making an angle of 45° with the y-axis as shown. Find the time
period of this vibratory motion?

While solving this problem, we
shall know a concept of slope of the graph is nothing but equal to the ratio of opposite
side by adjacent side of the graph. By applying that concept we can get that
slope is nothing but equal to 1. By comparing this value with the standard value
of a body in simple harmonic motion we can derive the equation for the time
period as shown below.

**Problem five and solution**

The displacement of a body in
a simple harmonic motion is as shown below find its initial displacement and
maximum velocity of this case?

In solving this problem we shall
understand that a body in oscillatory motion can initially have some
displacement about its mean position. This kind of the displacement is actually
called initial displacement. The initial phase also helps in representing this
initial displacement. So while solving this problem we have two put time equal
to

**0**to get the initial displacement.**Problem six and solution**

A body is in simple harmonic
motion starting from the mean position.
Find the time taken by it to to move from

1.mean position to half of the amplitude,

2.mean position to amplitude,

3.from half of the amplitude to complete amplitude?

1.mean position to half of the amplitude,

2.mean position to amplitude,

3.from half of the amplitude to complete amplitude?

While solving this equation we
can use the basic equation of the displacement that we had derived for a body
in simple harmonic motion. As per the demand of the problem in the place of the
displacement we can write anything in terms of the amplitude as per the given
data.

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