Gives the x-t plot of a particle executing one-dimensional simple… - Vidyadip

Question

Gives the x-t plot of a particle executing one-dimensional simple harmonic motion. (You will learn about this motion in more detail in Chapter 14). 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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Answer

For simple harmonic motion (SHM) of a particle, acceleration (a) is given by the relation: $\text{a}=-\omega^2\text{x}$ Where $\omega$ = angular frequency t = 0.3s 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. t = 1.2s 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. t = – 1.2s In this time interval, x is negative. Now the slope of the x-t plot is positive. Therefore, position is negative and velocity is positive. Acceleration of the particle using (i) will be positive.

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