Oscillations Te...

The equation of a damped simple  harmonic motion is $$m\frac{d^{2}x}{dt^{2}}+b\frac{dx}{dt}+kx=0$$. Then the angular frequency of oscillation is 

A paramedical staff nurse improvises a second's pendulum (time period 2 s) by fixing one end of a string of length $$L$$ to a ceiling and the other end to a heavy object of negligible size. Within 60 oscillations of this pendulum, she finds that the pulse of a wounded soldier beats 110 times. A symptom of bradycardia is pulse $$< 60$$ per minute and that of tachycardiais $$> 100$$ per minute. Then the length of the string is nearly symptoms of 

A bob of a simple pendulum executing SHM in air has time period $$T_o$$ and in water has time period T. Neglect friction. Relation between T and $$T_o$$ if density of bob is $$4/3 \times 10^3 kg/m^3$$, is

Two graphs of the same harmonic wave are shown below. The graph (1) on the left shows the displacement of wave y, as a function of position x for a given instant of time. The graph (2) on the right shows the displacement of a wave as a function of time 't' for a given position. The speed of the wave is 

A simple pendulum with  a bob of mass m swings with angular amplitude of $$60^o$$, when its angular displacement $$30^o$$, find the tension of string

The mass of the bob of a simple pendulum of length L is m. If the bob is left from its horizontal position then the speed of the bob and the tension in the thread at the lowest position of the bob will be respectively :-

A simple pendulum is vibrating with an an angolar amplitude of $$90 ^ { \circ }$$,For what values of   with vertical, the accelcration is directed 
In sertically upwards
2) horizontally
vertically downwerds

A simple harmonic motion is given by $$ y= 5 ( sin 3\pi  t +\sqrt3 cos 3 \pi t)$$. What is the amplitude of motion if y in m?

Under the action of a force $$ F = -kx^3$$, the motion of a particle is ($$k$$= a positive constant)

A particle of mass m moving in a one-dimensional potential energy $$U(x) = -ax^{2} + bx^{4}$$, where 'a' and 'b' are positive constants. The angular frequency of small oscillations about the minima of the potential energy is equal to