Procedure for the experiment is as follows:

1.To study the Simple harmonic motion

• step1: Read the theory

• step2: Set the damping factor (b) = 0

• step3: set v_o= 0 m/s

• step4: Drag the ball to maximum starting position say x_o= 10.0m and play the animation button.

• step5: Observe the graph,wait until the animation ends

Graph representing S.H.M motion (position graph)



Graph representing S.H.M motion (position and velocity graph)

2.To study Damped oscillatory motion

• step1: Reset the simulation

• step2: Set v_o= 0 m/sec

• step3: change the damping factor(b) from 0 to some value take three cases and reset the simulation in each case

• Case 1:Under-Damping

Set the value of b < 2√2 (say b= 0.5)

Graph representing under-damped oscillatory motion (position graph)



Graph representing under-damped oscillatory motion (position and velocity graph)



• Case 2: Critical-Damping

Set the value of b = 2√2

Graph representing critical-damped oscillatory motion (position graph)



Graph representing critical-damped oscillatory motion (position and velocity graph)



• Case 3: Over-Damping

Set the value of b > 2√2 (say b= 3)

Graph representing over-damped oscillatory motion (position graph)



Graph representing over-damped oscillatory motion (position and velocity graph)



• step4: Drag the ball to maximum starting position say x_o= 10.0m and play the animation button.

• step5: In all the above three cases mentioned observe the graph and wait till animation ends.

3.To study Forced oscillatory motion

• step1: Reset the simulation again

• step2: Set the damping coefficient (b) > 2√2

• step3: Change the value of initial velocity v_o= 2m/sec

• step4: Set value of driven frequency(ω) = 1.41

• step5: Set some value of driven amplitude F_o which will be the force for oscillation

• step6: Drag the ball to maximum starting position say x_o= 10.0m and play the animation button.

• step7: Observe the graph till the animation ends

Graph representing forced-oscillatory motion (position graph)



Graph representing forced-oscillatory motion (position and velocity graph)

Perform the following experiments

Experiment-1:

Perform experiment to calculate the value of k (spring constant) in the following cases described below.In each case record observations into the table and compute the value of k.Take value of m =1 kg in each case.

• Case 1: Free oscillator (simple harmonic motion) when b = 0

1. set different values for x_o

2. keep other parameters = 0

3. record the value of time in each case

4. calculate corrosponding angular frequency

5. then compute k (spring constant) using formula
   
   

S.no	xo (displacement)	f (frequency)	ω (angular frequency)
1.
2.
3.
4.
5.
6.

The mean ω: _________

• Computed value of k:__________




• Case 2:Under-Damped damped Oscillator when b < 2√2

1. set different values for x_o

2. set b<2√2 and keep other parameters = 0

3. record the value of time in each case

4. calculate corrosponding angular frequency:

   
   

5. Value of b used in the experiment:_________

S.no	xo (displacement)	f (frequency)	ω (angular frequency)
1.
2.
3.
4.
5.
6.

• The mean = ________

• computed value of k=_____________

Case 3: Forced oscillator when b > 2√2

1. set different values for F_o

2. set driven frequency ω =1rad/sec,

3. obtain the value of amplitude by observing graph each time.

4. obtain the value of ω using the relation:

   

5. then compute k (spring constant) from the calculated mean value of




S.no	Fo (force)	A (amplitude)	ω (angular frequency)
1.
2.
3.
4.
5.
6.

• The mean ω = ________

• computed value of k =_____________