Figure 3.23 gives the x-t plot of a particle executing a 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.
Fig. 3.23
For simple harmonic motion (SHM) of a particle, acceleration (a) is given by the relation:
a = – ω2x .......(i)
Where ω = angular frequency
at, t=0.3 s
In this time interval, x is negative. Now the slope of the x-t plot is negative. Therefore, both position and velocity are negative. Acceleration of the particle using (i) will be positive.
at, t=1.2 s
In this time interval, x is positive. Now the slope of the x-t plot is positive. Therefore, both position and velocity are positive. Acceleration of the particle using (i) will be negative.
at, t=-1.2 s
In this time interval, x is negative. Now the slope of the x-t plot is positive. Therefore, the position is negative and velocity is positive. Acceleration of the particle using (i) will be positive.
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