Fig 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 particles at ` t= 0.3 s`, ` 1.2 s, - 1. 2 s`,

Explanation

Negative, Negative, Positive (at t = 0.3 s)
Positive, Positive, Negative (at t = 1.2 s)
Negative, Positive, Positive (at t = –1.2 s)
For simple harmonic motion (SHM) of a particle, acceleration (a) is given by the relation:
`a=-w^2xxwto` angular frequency ... (i)
t=0.3 s
In this time interval, x is negative. Thus, the slope of the x-t plot will also be negative. Therefore, both position and velocity are negative. However, using equation (i), acceleration of the particle will be positive.
t = 1.2 s
In this time interval, x is positive. Thus, 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. Thus, the slope of the x–t plot will also be negative. Since both x and t are negative, the velocity comes to be positive. From equation (i), it can be inferred that the acceleration of the particle will be positive.