A particle starts from a point $P$ at a distance of $A/2$ from the mean position $O\, \&$ travels towards left as shown in the figure. If the time period of $SHM,$ executed about $O$ is $T$ and amplitude $A$ then the equation of motion of particle is :
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A $1 \,kg$ block attached to a spring vibrates with a frequency of $1\, Hz$ on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an $8\, kg$ block placed on the same table. So, the frequency of vibration of the $8\, kg$ block is ..... $Hz$
At a given point of time the value of displacement of a simple harmonic oscillator is given as $y = A \cos \left(30^{\circ}\right)$. If amplitude is $40\,cm$ and kinetic energy at that time is $200\, J$, the value of force constant is $1.0 \times 10^{ x }\,Nm ^{-1}$. The value of $x$ is ......
A particle is placed at the lowest point of a smooth wire frame in the shape of a parabola, lying in the vertical $xy-$ plane having equation $x^2 = 5y$ $(x, y$ are in meter). After slight displacement, the particle is set free. Find angular frequency of oscillation.....$rad/s$ (in $rad/sec$ ) (take $g = 10\ m/s^2$ )
A particle is performing simple harmonic motion along $x-$axis with amplitude $4 \,cm$ and time period $1.2\, sec$. The minimum time taken by the particle to move from $x =2 ,cm$ to $ x = + 4\, cm$ and back again is given by .... $\sec$
A particle executes simple harmonic motion with an amplitude of $4 \,cm$. At the mean position the velocity of the particle is $10\, cm/s$. The distance of the particle from the mean position when its speed becomes $5 \,cm/s$ is
The maximum velocity of a body undergoing $S.H.M$. is $0.2\,m/s$ and its acceleration at $0.1\,m$ from the mean position is $0.4\,m/s^2$. The amplitude of the $S.H.M.$ is .... $m$