An object has a mass of 0.5 kg. It undergoes a simple harmonic motion. The amplitude of that motion is 0.07 m and the period is 0.31 s. What is the total energy of the object?
0.5 J
To find the total energy of the object undergoing simple harmonic motion, we need to know two things: the mass of the object (m) and the frequency of the motion (f).
First, let's find the frequency (f) using the period (T) of the motion. The formula to find the frequency is:
f = 1/T
Given that the period (T) is 0.31 seconds, we can calculate the frequency (f) as follows:
f = 1/0.31 s
f ≈ 3.23 Hz
Next, we need to find the angular frequency (ω) using the formula:
ω = 2πf
Given that the frequency (f) is approximately 3.23 Hz, we can calculate the angular frequency (ω) as follows:
ω = 2π × 3.23 Hz
ω ≈ 20.3 rad/s
Now that we have the mass (m = 0.5 kg) and the angular frequency (ω ≈ 20.3 rad/s), we can find the total energy (E) of the object using the formula:
E = (1/2) m ω² A²
Given that the amplitude (A) is 0.07 m, we can calculate the total energy (E) as follows:
E = (1/2) × 0.5 kg × (20.3 rad/s)² × (0.07 m)²
E ≈ 0.123 Joules
Therefore, the total energy of the object undergoing simple harmonic motion is approximately 0.123 Joules.