Oscillations Te...

A block of mass $$M$$ is performing $$SHM$$ with amplitude $$A$$ on a smooth horizontal surface$$.$$ At the extreme position a small block of mass $$m$$ falls vertically and sticks to$$M.$$ then$$,$$ amplitude of oscillation will be                                               

A particle of mass $$m$$ is allowed to oscillate on a smooth parabola: $${ x }^{ 2 }=4ay,a>1$$ as shown in the  figure. The angular frequency $$\left( \omega  \right) $$ of small oscillations is 
 

As shown in figure a horizontal platform with a mass $$m$$ placed on it is executing SHM along y-axis. If the amplitude of oscillation is $$2.5cm$$, the minimum period of the motion for the mass not to be detached from the platform is 
($$g=10m/{sec}^{2}={\pi}^{2}$$)

A horizontal plank has a rectangular block placed on it. The plank starts oscillating vertically and simple harmonically with an amplitude of $$40\ cm$$. The block just loses contact with the plank when the latter is at momentary rest. Then

$$ABC$$ is an equilateral triangle structure up of a light rigid material. Find the frequency of small vertical oscillations of mass $$m$$ along $$AG$$. Conisider $${k}_{1}={k}_{2}={k}_{3}={k}_{4}=k$$

The length of simple pendulum is about 100 cm known to have an accuracy of 1 mm. Its period of oscillation is 2 s determined by measuring the time for 100 oscillations using a block of 0.1 s resolution. What is the accuracy in the determined value g?

A spring is placed in vertical position by suspending it from a hook at its top. A similar hook on the bottom of the spring is at $$11\ cm$$ above a table top. A mass of $$75\ g$$ and of negligible size is then suspended from the bottom hook, which is measured to be $$4.5\ cm$$ above the table top. The mass is then pulled down a distance of $$4\ cm$$ and released. Find the approximate position of the bottom hook after $$s$$?
Take $$g=10m/{s}^{2}$$ and hooks mass to be negligible.

A particle executing S.H.M. given by equation $$ y= 8 sin 6 \pi t $$ is sending out waves in a continuous medium traveling at 200 cm/s. the resultant displacement of the particle 150 cm, from B and one second after commencement of vibration of B is:

A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time in seconds is:

A simple pendulum of length 1 m is oscillating with an angular frequency 10 rad/s. The support of the pendulum starts oscillating up and down with a small angular frequency off 1 rad/s and an amplitude of $${ 10 }^{ -2 }.$$ The relative change in the angular frequency of the pendulum is best given by: