KVPY2010PhysicsOscillations
A particle of mass m under goes oscillations about x =0 in a potential given by V ( x )= 1 2 kx ²- V ₀ ( x a ) , where V₀, k , a are constants. If the amplitude of oscillation is much smaller than a, the time period is given by-
Options
- A2 m a² k a²+V₀
- B2 m k
- C2 ma ² ~V ₀
- D2 m a² k a²-V₀
Correct answer
A. 2 m a² k a²+V₀
Step-by-step solution
array l V(x)= 1 2 k x²-V₀ ( x a ) E=- d V d x =- (k x+V₀ ( x a ) 1 a ) array since x< < a ( x a ) x a or E =- ( k + V ₀ a ² ) x This resembles F =- kx array l T =2 m k =2 ma ² ka ²+ v ₀ =2 m a ² ka ²+ v ₀ array