A body executing linear simple harmonic motion has a velocity of $3 c m / s$ , when its displacement is $4 c m$ and a velocity of $4 c m / s$ , when its displacement is $3 c m$ . What is the amplitude of oscillation?

5 c m

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

7.5 c m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

10 c m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

12.5 c m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $5 c m$
In SHM, the velocity $V$ at a displacement $x$ is given by
$V = ω {(A^{2} - x^{2})}^{\frac{1}{2}} o r V^{2} = ω^{2} (A^{2} - x^{2})$
Now
$V = 3 c m / s$
When,
$x = 4 c m . ∴ 9 = ω^{2} (A^{2} - 16) . . . . . . (i)$

Also
$V = 4 c m / s$
When,
$x = 3 c m ∴ 16 = ω^{2} (A^{2} - 9) . . . . . . (i i)$
Simultaneous solution of equations $(i)$ and $(i i)$ gives
$A = 5 c m$

Suggest Corrections

Similar questions

Q. A body executing linear simple harmonic motion has a velocity of

3 c m / s

, when its displacement is

4 c m

and a velocity of

4 c m / s

, when its displacement is

3 c m

. What is the amplitude of oscillation?

Q. A body executing SHM has its velocity

10 c m / s

and

7 c m / s

when its displacements from mean position are

3 c m

and

4 c m

respectively. The length of path is

A body describes simple harmonic motion with amplitude of 5 cm and a period of 0.2 s. Find the acceleration and velocity of the body when the displacement is (a) 5 cm, (b) 3 cm, (c) 0 cm.

Q. A particle is executing simple harmonic motion with an amplitude of

4 c m

. At the mean position the velocity of the particle is

10 c m / s

. The distance of the particle from the mean position when its speed becomes

5 c m / s

A body is executing simple harmonic motion with an angular frequency 2rad/s. The velocity of the body at 20 mm displacement, when the amplitude of motion is 60 mm, is

[CPMT 1999]

Join BYJU'S Learning Program

A body executing linear simple harmonic motion has a velocity of 3 cm/s, when its displacement is 4 cm and a velocity of 4 cm/s, when its displacement is 3 cm. What is the amplitude of oscillation?

The correct option is A 5 cmIn SHM, the velocity V at a displacement x is given by V=ω(A2−x2)12or V2=ω2(A2−x2) Now V=3 cm/s When, x=4 cm.∴9=ω2(A2−16)......(i) Also V=4cm/s When, x=3 cm∴16=ω2(A2−9)......(ii) Simultaneous solution of equations (i) and (ii) gives A=5 cm

A body executing linear simple harmonic motion has a velocity of $3 c m / s$ , when its displacement is $4 c m$ and a velocity of $4 c m / s$ , when its displacement is $3 c m$ . What is the amplitude of oscillation?