Oscillations Te...

We are still looking at the oscillating thingy hanging from a spring. The system was set vibrating by pulling the thingy down below its equilibrium position and then letting it go from rest. If the initial displacement is doubled what happens to the maximum kinetic energy of the thing?

The displacement of a particle is represented by the equation $$y=3 cos(\dfrac{\pi}{4}- 2 \omega t)$$. The motion of the particle is :

A particle executing SHM has a maximum speed of $$0.5 m{s}^{-1}$$ and maximum acceleration of $$1 m {s}^{-2}$$. 

In their discussions of SHM text books sometimes consider a thingy attached to a horizontal spring and moving horizontally on a frictionless surface, instead of the hanging thingy that we have been looking at. Suppose that the two springs and the two thingies are identical. Think about whether these two systems are significantly different in other respects and decide which one of the following statements is true.

Which of  the  following regarding oscillatory motion is true?

Which of the following is an example of oscillatory motion? 

A mass of 2.0 kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released the mass executes a simple harmonic motion. The spring constant is 200 N/m. What should be the minimum amplitude of the motion, so that the mass gets detached from the pan?
(Take $$\displaystyle g=10{ m }/{ { s }^{ 2 } }$$)

Which of the following conditions must be satisfied for a body to oscillate or vibrate?
A: The body must have inertia to keep it moving across the mid point of its path.
B: There must be a restoring force to accelerate the body towards the midpoint.
C: The fractional force acting on the body against its motion must be small.

The displacement of a particle is represented by the equation $$y=sin^3(\omega t)$$. The motion is 

The velocity  vector $$v$$ and displacement vector $$x$$ of a particle executing SHM are related as $$\dfrac{v dv}{dx} ={\omega}^2 x$$ with the initial condition $$v = v_0$$ at  $$x = 0$$. The velocity $$v$$, when displacement is $$x$$, is: