An object has a mass of 0.3
kg. It undergoes a simple harmonic motion. The amplitude of that motion is 0.09
m and the period is 0.36 s. What is the total energy of the object?
my answer: 4.11 J
-period=1/f.
- omega=2*pi*f=17.45
only kinetic energy therefore Etotal=1/2mv^2=1/2*m*A*omega^2
=4.11 J
To find the total energy of an object undergoing simple harmonic motion, you can use the formula:
Etotal = 1/2 * m * A^2 * ω^2
Where:
Etotal is the total energy
m is the mass of the object
A is the amplitude of the motion
ω is the angular frequency
Given:
m = 0.3 kg (mass of the object)
A = 0.09 m (amplitude of the motion)
T = 0.36 s (period of the motion)
First, we need to find the angular frequency ω. The angular frequency is given by the formula:
ω = 2π / T
where T is the period of the motion. Substituting the given values:
ω = 2π / 0.36 s ≈ 17.45 rad/s
Now, we can substitute the values of m, A, and ω into the formula for total energy:
Etotal = 1/2 * 0.3 kg * (0.09 m)^2 * (17.45 rad/s)^2
Etotal ≈ 4.11 J
Therefore, the total energy of the object undergoing simple harmonic motion is approximately 4.11 Joules.