KCET2023PhysicsOscillations
A block of mass m is connected to a light spring of force constant k . The system is placed inside a damping medium of damping constant b . The instantaneous values of displacement, acceleration and energy of the block are x, a and E respectively. The initial amplitude of oscillation is A and ^ is the angular frequency of oscillations. The incorrect expression related to the damped oscillations is
Options
- Ax=A e^ - b m ( ^ t+ )
- B^ = k m - b^2 4 m^2
- CE= 1 2 k A^2 e^ - b t m
- Dm d^2 x d t^2 +b d x d t +k x=0
Correct answer
A. x=A e^ - b m ( ^ t+ )
Step-by-step solution
Equation of motion for damped oscillation is m d^2 x d t^2 + b d x d t +k x=0 Angular frequency is ^ = k m - b^2 4 m^2 Displacement is given by, x=A₀ e^ - b 2 m t ( t+ ) and energy is given by E= 1 2 k A^2 e^ - b m t