Question

Figure 3.23 gives the x-t plot of a particle executing one-dimensional simple harmonic motion. (You will learn about this motion in more detail in Chapter14). Give the signs of position, velocity and acceleration variables of the particle at t = 0.3 s, 1.2 s, – 1.2 s. 

Answer 1

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 = – ω²x ω → 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