A 45 g mass is attached to a massless spring and allowed to oscillate around an equilibrium according to:
y(t) = 1.3 * sin( 0.6 * t ) where y is measured in meters and t in seconds.
(a) What is the spring constant in N/m?
k = N/m
.162 NO
HELP: You are given m, the mass. What other quantity appears in the equation involving k, the spring constant, and m?
HELP: You are given the equation of motion
y(t) = A * sin( ω * t )
Now can you find the missing quantity?
No one has answered this question yet.
To find the spring constant (k) in N/m, you need to use the equation of motion provided, as well as the given mass (m) and a few other formulas.
The equation of motion given is: y(t) = A * sin(ω * t)
In this equation, "A" represents the amplitude and "ω" represents the angular frequency.
Comparing this equation to the given equation: y(t) = 1.3 * sin(0.6 * t), we can see that the amplitude (A) is 1.3.
Now, we need to determine the angular frequency (ω). The angular frequency is related to the spring constant (k) and the mass (m) by the equation: ω = √(k/m).
Since we know the mass (m) is 45 g, we need to convert it to kilograms (kg) by dividing it by 1000: m = 45 g / 1000 = 0.045 kg.
Now we can rearrange the equation ω = √(k/m) to solve for the spring constant (k). Squaring both sides gives us: ω^2 = k/m.
Substituting the given angular frequency (ω = 0.6) and the mass (m = 0.045 kg) into the equation, we get: 0.6^2 = k / 0.045.
Simplifying this equation, we find: 0.36 = k / 0.045.
To isolate k, we can multiply both sides of the equation by 0.045: 0.36 * 0.045 = k.
Calculating this, we find: k = 0.0162 N/m.
Therefore, the spring constant (k) is 0.0162 N/m.