Oscillations Te...

If a simple pendulum has significant amplitude (up to a factor of 1/e of original) only in the period between t = 0s to t = τs, then τ may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with \'b\' as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds

Two springs of spring constants k₁ and k₂ are connected as shown. The effective spring constant k_e =

The mass M shown in the figure oscillates in simple harmonic motion with amplitude A. The amplitude of the point P is

Two identical springs of constant K are connected in series and parallel as shown in figure. A mass m is suspended from them. The ratio of their frequencies of vertical oscillations will be

A mass m is suspended from the two coupled springs connected in series. The force constant for springs are K₁. and K₂. The time period of the suspended mass will be

A weightless spring which has a force constant oscillates with frequency n when a mass m is suspended from it. The spring is cut into two equal halves and a mass 2 m is suspended from it. The frequency of oscillation will now become

A mass M is suspended from a light spring. An additional mass m added displaces the spring further by a distance x. Now the combined mass will oscillate on the spring with period

A particle of mass 200 gm executes S.H.M. The restoring force is provided by a spring of force constant 80 N/m. The time period of oscillations is

The length of a spring is l and its force constant is k. When a weight W is suspended from it, its length increases by x. If the spring is cut into two equal parts and put in parallel and the same weight W is suspended from them, then the extension will be