Direct use of the equation of simple harmonic motion:[Oscillations Patterns of problems Part 1/8]

 Direct use of the equation of simple harmonic motion

In this type of problems, direct use of the equation of simple harmonic motion is the key. Suppose we have one equation of SHM in our hands. Now, if we compare this equation with the standard equation of SHM then we can easily find the amplitude, frequency etc. of that particular SHM. Let us see some examples.

 [Difficult level: M-Medium , E-Easy , H-Hard] 

 Question:  From NCERT  | NEET   || [Difficult level:M] ||| 

.

The motion of a particle varies with time according to the relation $y=a\sin$$\omega$$t+a\cos$$\omega t$ . Then

A

the motion is oscillatory but not SHM

B

the motion is SHM with amplitude $a$

C

the motion is SHM with amplitude $a\; root$ $2$

D

the motion is SHM with amplitude 2a​

.

.

 ✅ 

 Answer ▽ ✅Verified 

C

the motion is SHM with amplitude $a\; root$ $2$

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 Question:  From NCERT  | NEET   || [Difficult level:Easy] ||| 

.

A mass m=100 gms is attached at the end of a light spring which oscillates on a friction less horizontal table with an amplitude equal to 0.16 meter and the time period equal to 2 sec. Initially the mass is released from rest at t=0 and displacement x=−0.16 meter. The expression for the displacement of the mass at any time (t) is 

A

x=0.16cos(πt)

B

x=−0.16cos(πt)

C

x=0.16cos(πt+π)

D

x=−0.16cos(πt+π)

.

.

 ✅ 

 Answer ▽ ✅Verified 

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