The equation of motion of a particle is $x = a\,cos (\alpha\, t)$ . The motion is
A
Periodic but not oscillatory
B
Periodic and oscillatory
C
Oscillatory but not periodic
D
Neither periodic nor oscillatory
Medium
Download our app for free and get started
B
Periodic and oscillatory
b
Download our app
and get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
A body executing $S.H.M.$ along a straightline has a velocity of $3 \,ms ^{-1}$ when it is at a distance of $4 \,m$ from its mean position and $4 \,ms ^{-1}$ when it is at a distance of $3 \,m$ from its mean position. Its angular frequency and amplitude are
The instantaneous displacement of a simple pendulum oscillator is given by $x = A\cos \left( {\omega t + \frac{\pi }{4}} \right)$. Its speed will be maximum at time
The variation of kinetic energy $(KE)$ of a particle executing simple harmonic motion with the displacement $(x)$ starting from mean position to extreme position $(A)$ is given by
A body executes simple harmonic motion. The potential energy $(P.E.)$, the kinetic energy $(K.E.)$ and total energy $(T.E.)$ are measured as a function of displacement $x$. Which of the following statements is true
A mass $m$ is suspended from the two coupled springs connected in series. The force constant for springs are ${K_1}$ and ${K_2}$. The time period of the suspended mass will be
A mass $m$ attached to free end of a spring executes SHM with a period of $1\; s$. If the mass is increased by $3\; kg$ the period of oscillation increases by one second, the value of mass $m$ is $..............kg$.
The time period of a particle executing $S.H.M.$ is $8 \,s$. At $t=0$ it is at the mean position. The ratio of distance covered by the particle in $1^{\text {st }}$ second to the $2^{\text {nd }}$ second is .............. $s$