The displacement of a damped harmonic oscillator is given by x(t ) = e-0.1t cos (10πt + φ). Here t is in seconds. The time taken for its amplitude of vibration to drop to half of its initial value is close to :
Options

Question

The displacement of a damped harmonic oscillator is given by x(t ) = e-0.1t cos (10πt + φ). Here t is in seconds. The time taken for its amplitude of vibration to drop to half of its initial value is close to :

Options

G1 Physics · Accepted Answer

The amplitude envelope is e^(−0.1t). Setting e^(−0.1t)=1/2 gives t=ln2/0.1≈6.93 s≈7 s. Hence option B.

The displacement of a damped harmonic oscillator is given by x(t ) = e−0.1t cos (10πt + φ). Here t is in seconds. The time taken for its amplitude of vibration to drop to half of its initial value is close to :