Figure gives the x-t plot of a particle executing one-dimensional simple harmonic motion. Give the signs of position, velocity and acceleration variables of the particle at $t = 0.3 s, 1.2 s, - 1.2 s .$

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Solution

For simple harmonic motion (SHM) of a particle, acceleration (a) is given by the relation:
$a = - ω^{2} x . . . . . . . . . . . . . . (i)$
$ω$ is angular frequency
$t = 0.3 s$
$x$ is negative. The slope of the x-t plot is also negative. Therefore, both position and velocity are negative. However, using equation (i), acceleration of the particle will be positive.
$t = 1.2 s$
x is positive. The slope of the x-t plot will also be positive. Therefore, both position and velocity are positive. However, using equation (i), acceleration of the particle comes to be negative.
$t = - 1.2 s$
In this time interval, x is negative. The slope of the x-t plot is positive. Hence, the velocity comes to be positive. From equation (i), it can be inferred that the acceleration of the particle will be positive.

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Figure gives the x-t plot of a particle executing one-dimensional simple harmonic motion. Give the signs of position, velocity and acceleration variables of the particle at t=0.3s,1.2s,−1.2s.

Figure gives the x-t plot of a particle executing one-dimensional simple harmonic motion. Give the signs of position, velocity and acceleration variables of the particle at $t = 0.3 s, 1.2 s, - 1.2 s .$