wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A weakly damped harmonic oscillator is executing resonant oscillations. The phase difference between the oscillator and the external periodic force is:

A
Zero
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
π/4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
π/2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
π
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C π/2
The equation for forced oscillation in a damped system is given as-
md2xdt2+bdxdt+kx=F0cosωt
Dividing by m throughout,
d2xdt2+2βdxdt+ω20x=Acosωt
The expected solution is of form x=Dcos(ωtδ)
Put this is in above equation gives,
tanδ=2βωω20ω2
For resonant oscillation, ω0=ω
δ=π/2 which is the phase difference between x and F.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Expression for SHM
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon