The composition of two simple harmonic motions of equal periods at right angle to each other and with a phase difference of $\pi $ results in the displacement of the particle along
AIPMT 1990, Medium
Download our app for free and get started
(a) If ${y_1} = {a_1}\sin \omega \,t$ and ${y_2} = {a_2}\sin (\omega \,t + \pi )$
==> $\frac{{{y_1}}}{{{a_1}}} + \frac{{{y_2}}}{{{a_2}}} = 0$
==> $\frac{{{y_1}}}{{{a_1}}} + \frac{{{y_2}}}{{{a_2}}} = 0$
==> ${y_2} = - \frac{{{a_2}}}{{{a_1}}}{y_1}$
This is the equation of straight line.
Download our appand 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
- 1Acceleration of a particle, executing $SHM$, at it’s mean position isView Solution
- 2The displacement of a particle is represented by the equation $y = sin^3\,\,\,\omega t$ . The motion isView Solution
- 3A rod of mass $m$ and length $l$ is suspended from ceiling with two string of length $l$ as shown. When the rod is given a small push in the plane of page and released time period is $T_1$ and when the rod is given a push perpendicular to plane time period of oscillation is $T_2$ . The ratio $\frac{{T_1^2}}{{T_2^2}}$ isView Solution
- 4A pendulum is executing simple harmonic motion and its maximum kinetic energy is $K_1$. If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is $K_2$ thenView Solution
- 5Spring of spring constant $1200\, Nm^{-1}$ is mounted on a smooth frictionless surface and attached to a block of mass $3\, kg$. Block is pulled $2\, cm$ to the right and released. The angular frequency of oscillation is .... $ rad/sec$View Solution
- 6A particle moves with simple harmonic motion in a straight line. In first $\tau \,s$, after starting from rest, it travels a distance $a$, and in next $\tau \,s$, it travels $2a$ in same direction thenView Solution
- 7The period of a simple pendulum measured inside a stationary lift is found to be $T$. If the lift starts accelerating upwards with acceleration of $g/3,$ then the time period of the pendulum isView Solution
- 8The $x$-t graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at $t=4 / 3 \mathrm{~s}$ isView Solution
- 9Two bodies performing $SHM$ have same amplitude and frequency. Their phases at a certain instant are as shown in the figure. The phase difference between them isView Solution
- 10A particle has simple harmonic motion. The equation of its motion is $x = 5\sin \left( {4t - \frac{\pi }{6}} \right)$, where $x$ is its displacement. If the displacement of the particle is $3$ units, then it velocity isView Solution