A 1.2kg mass attached to spring oscillates with an amplitude of 5.1cm and frequency 1.2Hz what is its energy of motion
omega = 2 pi f = sqrt (k/m)
2 pi * 1.2 = 7.54 = sqrt (k/1.2)
k/1.2 = 56.8
k = 68.1
at max amplitude speed = 0 so total energy = (1/2) k x^2
=(1/2) (68.1) (0.051)^2 = 0.0886 Joules
To find the energy of motion of the oscillating mass, you can use the equation for the energy of a simple harmonic oscillator:
E = (1/2) * k * A^2,
where E is the energy, k is the spring constant, and A is the amplitude of the oscillation.
To find the spring constant, you can use the formula:
k = (2 * π * f)^2 * m,
where k is the spring constant, f is the frequency, and m is the mass.
Given:
Mass (m) = 1.2 kg
Amplitude (A) = 5.1 cm = 0.051 m
Frequency (f) = 1.2 Hz
Let's calculate the spring constant (k) first:
k = (2 * π * f)^2 * m
= (2 * π * 1.2)^2 * 1.2
≈ 9.137 N/m.
Now, using the equation for energy:
E = (1/2) * k * A^2
= (1/2) * 9.137 * 0.051^2
≈ 0.0055 Joules.
Therefore, the energy of motion of the oscillating mass is approximately 0.0055 Joules.