Damped Oscillation

There is a LCR circuit , If it is compared with a damped oscillation of mass m oscillating with force constant k and damping coefficient 'b'. Compare the terms of damped oscillation with the devices in LCR circuit.

A vibrating system consists of mass 12.5 kg, a spring of spring constant 1000 (N ) /( m ) performing damped oscillation with damping coefficient of 15 kg s^(-1) . The value of critical damping coefficient of the system is

A particle is performing damped oscillation with frequency 5Hz . After every 10 oscillations its amplitude becmoes half. Find time from beginning after which the amplitude becomes 1//1000 of its initial amplitude :

In damped oscillation mass is 1 kg and spring constant = 100 N/m, damping coefficient = 0.5 kg s^(–1) . If the mass is displaced by 10 cm from its mean position that what will be the value of its mechanical energy after 4 seconds ?

A circuit with capacitance C and inductance L generates free damped oscillations with current varying with time as I=I_(m)e^(-betat) sin omegat . Find the voltage across the capacitor as a function of time, and in particular, at the moment t=0 .

The free damped oscillations are maintained in a circuit, such that the voltage across the capacitor varies as V=V_(m)theta^(betat) cos omegat , Find the moments of time when the modulus of the voltage across the capacitor reaches (a) peak values, (b) maximum ( extremum ) values.

A point performs damped oscillations with frequency omega and damping coefficient beta according to the (4.1b). Find the initial amplitude a_(0) and the initial phase alpha if at the moment t=0 the displacement of the point and its velocity projection are equal to (a) x(0)=0 and u_(x)(0)=dot(x_(0)) , (b) x(0)=x_(0) and v_(x)(0)=0.

For a damped oscillator damping constant is 20gm/s, mass is 500gm. Find time taken for the amplitude to become half the initial