AP EAMCET202018 Sep 2020Evening ShiftPhysicsOscillationsActual
On a smooth inclined plane, a mass (M ) is attached between two massless springs of force constant (k ) each, as shown in the figure. The other ends of the springs are fixed to firm supports. The period of oscillation of the mass (M ) is
Options
- A(2 ( M 2 k )^ 1 2 )
- B(2 ( 2 M k )^ 1 2 )
- C(2 ( M g 2 k ) )
- D(2 ( 2 M g k )^ 1 2 )
Correct answer
A. (2 ( M 2 k )^ 1 2 )
Step-by-step solution
According to diagram given in question, it is clear that both springs are connected in series. ( ) Equivalent spring constant (k^ ) will be (k^ = k₁ k₂ k₁+k₂ = k k k+k = k 2 ) ...(i) Frequency of oscillation is given as (f= 1 2 k^ M ) ( ) Time period of oscillation, ( aligned T & = 1 f =2 M k^ T & =2 M k / 2 [from Eq.(i)] T & =2 2 M k =2 ( M 2 k )^ 1 / 2 aligned )