A body of unknown mass is attached to an ideal spring with force constant 113 N/m . It is found to vibrate with a frequency of 5.80 Hz .
A-Find the period.
B-Find the angular frequency.
C-Find the mass of the body.
To find the period, you can use the formula:
T = 1/frequency
where T is the period and frequency is given as 5.80 Hz.
A- Find the period:
T = 1 / 5.80 Hz = 0.1724 s
Therefore, the period is 0.1724 seconds.
Now, to find the angular frequency, you can use the formula:
ω = 2πf
where ω is the angular frequency and f is the frequency given as 5.80 Hz.
B- Find the angular frequency:
ω = 2π * 5.80 Hz = 36.47 radians/s
Therefore, the angular frequency is 36.47 radians/s.
The mass of the body can be found using the formula for the angular frequency of a mass-spring system:
ω = √(k/m)
where ω is the angular frequency, k is the force constant given as 113 N/m and m is the mass of the body which we need to find.
C- Find the mass of the body:
Rearranging the formula, we get:
m = k / ω²
m = 113 N/m / (36.47 radians/s)²
m = 113 N/m / 1328.2 radians²/s²
m = 0.085 kg
Therefore, the mass of the body is 0.085 kg.
To find the answers to these questions, you can use formulas related to simple harmonic motion and the properties of springs.
A - To find the period, you can use the formula T = 1/f, where T is the period and f is the frequency. In this case, the given frequency is 5.80 Hz, so you can substitute that into the formula to find the period.
T = 1 / 5.80 Hz
T ≈ 0.1724 s
Therefore, the period is approximately 0.1724 seconds.
B - The angular frequency, denoted by the symbol ω (omega), is related to the frequency by the equation ω = 2πf, where f is the frequency. You can plug in the given frequency to find the angular frequency.
ω = 2π * 5.80 Hz
ω ≈ 36.461 rad/s
Therefore, the angular frequency is approximately 36.461 radians per second.
C - The mass of the body is related to the force constant (k) of the spring and the angular frequency (ω) by the equation m = k / ω^2. You can substitute the given force constant and angular frequency to find the mass.
m = 113 N/m / (36.461 rad/s)^2
m ≈ 0.088 kg
Therefore, the mass of the body is approximately 0.088 kilograms.
A: .0172
B : 36.4