The motion of a particle represented by $y\ =$ $\sin \omega t - \cos \omega t$ is
Medium
Download our app for free and get startedPlay store
$y=\sqrt{2} \sin \left(\omega t-\frac{\pi}{4}\right)$

amplitude $\sqrt{2}$

$\mathrm{T}=\frac{2 \pi}{\omega}$

art

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.*

Similar Questions

  • 1
    A pendulum clock that keeps correct time on the earth is taken to the moon it will run (it is given that $g_{Moon} = g_{Earth}/6$ )
    View Solution
  • 2
    A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency $\omega $. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time
    View Solution
  • 3
    For a body executing $S.H.M. :$

    $(a)$ Potential energy is always equal to its $K.E.$

    $(b)$ Average potential and kinetic energy over any given time interval are always equal.

    $(c)$ Sum of the kinetic and potential energy at any point of time is constant.

    $(d)$ Average $K.E.$ in one time period is equal to average potential energy in one time period.

    Choose the most appropriate option from the options given below:

    View Solution
  • 4
    The position co-ordinates of a particle moving in a $3-D$ coordinates system is given by $x = a\,cos\,\omega t$ , $y = a\,sin\,\omega t$ and $z = a\omega t$ The speed of the  particle is
    View Solution
  • 5
    A particle is oscillating according to the equation $X = 7\cos 0.5\pi t$, where $t$ is in second. The point moves from the position of equilibrium to maximum displacement in time  ..... $\sec$
    View Solution
  • 6
    The angular velocity and the amplitude of a simple pendulum is $\omega $ and $a$ respectively. At a displacement $X$ from the mean position if its kinetic energy is $T$ and potential energy is $V$, then the ratio of $T$ to $V$ is
    View Solution
  • 7
    A block of mass $1 \,kg$ attached to a spring is made to oscillate with an initial amplitude of $12\, cm$. After $2\, minutes$ the amplitude decreases to $6\, cm$. Determine the value of the damping constant for this motion. (take In $2=0.693$ )
    View Solution
  • 8
    Two pendulums begins to swing simultaneously. The first pendulum makes $11$ full oscillations when the other makes $9$. The ratio of length of the two pendulums is
    View Solution
  • 9
    A $5\, kg$ collar is attached to a spring of spring constant $500\, Nm^{-1}$. It slides without friction over a horizontal rod. The collar is displaced from its equillibrium position by $10\, cm$ and released. The time period of oscillation is
    View Solution
  • 10
    A particle of mass $m$ is performing linear simple harmonic motion. Its equilibrium is at $x = 0,$ force constant is $K$ and amplitude of $SHM$ is $A$. The maximum power supplied by the restoring force to the particle during $SHM$ will be
    View Solution