Question

11
Which of the following equation does not represent
a simple harmonic motion :
(1) y = asinwt
(2) y = bcoswt
(3) y = asinwt+ bcoswt
(4) y = atanwt

Answer 1

Answer:

A simple harmonic motion, often termed as SHM is a type of periodic, oscillatory motion, where the force experienced by the object is directly proportional to the displacement from the mean position.

F ∝ (-x)

=> F = - kx, where k is a constant.

TRICK:

In order to find out the equation which doesn't represent SHM, you need to see if there is periodic nature of the equation.

"Sin" and "Cos" functions are periodic and represent SHM.

Option 1) and 2) are clearly periodic and represent SHM.

Option 3) can be simplified by calculation

as

y = {1/√(a²+b²)}[sin(ωt +θ)].

Now it becomes periodic and represents SHM.

But if you see option 4) closely,

"tan" function is NOT PERIODIC.

SO OPTION 4) DOESN'T REPRESENT SHM AND IS THE CORRECT ANSWER.

Answer 2

Answer:

Option : 4) y = atanwt .

Standard equation of SHM :

= d^2y = - w^2y .

dt^2

It is not satisfied by y = atanwt.

Oscillation :

an oscillation is in special type of periodic motion in which moves to and fro the fixed point called mean poistion of a particle .

Example: Click at Railway Station .

Simple Trick :

We have to see that if there is a periodic nature of equation .

'Sin' & "Cos' are functions that are Periodic and Represent SHM.

Therefore , Option (1) ,and Option (2) are that which are periodic and represent SHM.

Calculation of Option 3) :

y = { 1/√(a^2 + b^2)}[ sin ( wt + ø )] .

So, it becomes periodic and Represent SHM.

Now Option 4)

" Tan function is not periodic .

There is given to the tan function .

Therefore , Option 4) atanwt is that option which doesn't respresent a simple harmonic motion.