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.
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)