The displacement of a particle varies according to the relation x=4(cos⁡πt+sin⁡πt). The amplitude of the particle is

A particle's velocity is given by $v = 4 - 2t$, where $t$ is in seconds and $v$ is in m/s. If the particle starts at $x = 2$ m at $t = 0$, at what time does the particle instantaneously change its direction of motion?

A body undergoes SHM with an amplitude of $5$ cm. At a displacement of $3$ cm from the mean position, the magnitudes of its velocity and acceleration are equal. What is the time period of the SHM?

A simple pendulum performs simple harmonic motion about $\;X = 0$ with an amplitude A and time period $T$. The speed of the pendulum at $X = \frac{A}{2}$ will be

The speed of the particle on a reference circle of radius $R$ is $V$ . The time period of oscillations of the projection on a diameter of the circle is

The displacement y of a particle executing periodic motion is given by $y = 4{\cos ^2}\left( {t/2} \right)\sin \left( {1000t} \right)$ . This expression may be considered to be a result of the superposition of…….. independent harmonic motions

A body is vibrating in simple harmonic motion. If its acceleration is 12 ${\rm{cm}}{{\rm{s}}^{ - 2}}$ at a displacement 3 cm, then time period is

A simple pendulum swings back and forth. What is its average velocity over one complete swing?

A large horizontal surface moves up and down in SHM with an amplitude of 1 cm. if a mass of 10 kg (which is placed on the surface) is to remain continuously is in contact with it. The maximum frequency of SHM will be

The ratio of the magnitudes of maximum velocity to the maximum acceleration of a particle making $SHM$ is $1:1$. The minimum time taken by the particle to move between the extreme points of its path is

The displacement x(in metre) of a particle in simple harmonic motion is related to time t(in second) as $x = 0.01\cos \left( {\pi t + \frac{\pi }{4}} \right)$ The frequency of the motion will be