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.

Question

Philoid · Accepted Answer

The given figure represents simple harmonic motion (SHM).

Acceleration of a particle in simple harmonic motion is given by,

a = -ω²x ………….. (1)

Where,

a = acceleration/deceleration

ω = angular frequency

x = path distance

And v = r ω

Where,

v = velocity

r = radial distance

From above graph,

At t = 0.3 s (lies between t=0 and t=1),

Position, x is Negative,

Velocity, v is Negative (negative slope), and

Acceleration, a is Negative (from equation 1)

At t = 1.2 s (lies between t=1 and t=2),

Position, x is Positive,

Velocity, v is Positive (negative slope), and

Acceleration, a is Negative (from equation 1)

At t = -1.2 s (lies between t=1 and t=2),

Position, x is Negative,

Velocity, v is Positive (negative slope), and

Acceleration, a is Positive (from equation 1)

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.