Oscillations Te...

A particle moves in x-y plane according to the equation $$\overrightarrow {r  }   =(\hat { i } +2\hat { j })$$ $$A\, cos \,\omega t$$. The motion of the particle is 

A particles moves on the x-axis according to the equation $${ x=x }_{ 0 }{ sin }^{ 2 }\omega t$$. The motion is simple harmonic 

Periodic and Oscillatory Motions, Period and Frequency, Displacement
Identify the correct definition

A particle executes SHM in accordance with x = A sin $$\omega t.$$ If $${ t }_{ 1 }$$ is the time taken by it to reach from x = 0 to x = $$\sqrt { 3 } (A/2)$$ and $${ t }_{ 2 }$$ is the time taken by it to reach from x = $$\left( \sqrt { 3 } /2 \right) A$$ to x = A the value of $${ t }_{ 1 }/{ t }_{ 2 }$$ is 

The value of phase at   maximum displacement from  the mean position  of a particle in S.H.M. is 

On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is not correct?

A block of mass $$1 kg$$ is connected with a massless spring of force constant $$100 N/m$$. At $$t=0$$, a constant force $$F=10 N$$ is applied on the block. The spring is in its natural length at $$t=0$$. The speed of particle at $$x=6cm$$ from mean position is:

Potential energy of a particle of mass is given by $$U\quad =-\quad { U }_{ 0 }\left( 1-\cos {a x }  \right) .$$ which of the following can be a possible expression for its time period 

A particle executing SHM has max acceleration $$ 50 cm/s^2 $$ , The time period of oscillation of 2 sec and initial displacement 2.5 cm from the equilibrium position.The equation of SHM is $$ (take\ \pi^2 = 10) $$

The equation of an SHM with amplitude $$A$$ and angular frequency $$\omega$$ in which all the distances are measured from one extreme position and time is taken to be zero at the other extreme position is