Answer:
The displacement of the pendulum from equilibrium position is 0.855 of the length of the pendulum.
Explanation:
A pendulum's motion can be modelled as a simple harmonic motion and the differential equation describing simple harmonic motion is given as
(d²x/dt²) + (k/m)x = 0
(d²x/dt²) = acceleration of the pendulum
x = displacement of the pendulum from equilibrium position
k = spring constant of the pendulum = (mg/L) = (0.006×9.8/L) = (0.0588/L)
L = length of the pendulum
m = mass of the pendulum = 6 g = 0.006 kg
(k/m) = (g/L) = (9.8/L)
To calculate the pendulum's acceleration
Initial velocity of the car = 0 mph = 0 m/s
Final velocity of the car = 60 mph = 26.822 m/s
Time taken for velocity change = 3.2 s
Acceleration = (Δv/Δt) = (26.822/3.2) = 8.382 m/s²
(d²x/dt²) + (k/m)x = 0
Becomes
8.383 + (9.8/L)x = 0
(9.8x/L) = -8.382
9.8x = -8.382L
x = -(8.382/9.8) = -0.855 L (the minus sign shows the direction of movement of the pendulum)
Ignoring the sign and only focusing on the magnitude of the pendulum's displacement from equilibrium position, the displacement of the pendulum from equilibrium position is 0.855 of the length of the pendulum.
Hope this Helps!!!
