Three different weights are suspended from three different springs. Each spring has an elasticity coefficient of 18.5. The equation for the vertical displacement is y= 1.5cosine(t times the square root of k/m), where t is time, k is the elasticity coefficient, and m is the mass of the weight. Find the period and frequency of the spring if the weight has a mass of .4 kilogram.
wt= tsqrt(k/m)= 2pi*f*t=2PIf/T
you know sqrt(k/m) solve for f, T
Thanks so much! My teacher never gave is that equation. She just told us to go home and try to learn the method.
To find the period and frequency of the spring, we need to use the equation for the vertical displacement of the weight:
y = A * cosine(t * sqrt(k/m))
Where:
- y is the vertical displacement of the weight.
- A is the amplitude of the oscillation (which is not given in the question).
- t is the time.
- k is the elasticity coefficient of the spring.
- m is the mass of the weight.
In this case, we are given that the elasticity coefficient, k, is 18.5 and the mass of the weight, m, is 0.4 kg.
To find the period, we need to determine the value of time, t, at which the cosine function completes one full cycle. This will be the time period, denoted as T.
For a cosine function, one full cycle is completed when the argument of the cosine function increases by 2π radians. In this case, the argument is t * sqrt(k/m), so we need to solve the following equation for T:
t * sqrt(k/m) = 2π
Rearranging the equation, we get:
t = (2π) / sqrt(k/m)
Substituting the given values, we have:
t = (2π) / sqrt(18.5/0.4)
Evaluating the right side of the equation gives:
t ≈ 5.473 seconds (rounded to three decimal places)
Therefore, the period of the spring is approximately 5.473 seconds.
To find the frequency, which is the reciprocal of the period, we can use the formula:
Frequency (f) = 1 / T
Substituting the value of the period we calculated:
f ≈ 1 / 5.473 ≈ 0.183 Hz (rounded to three decimal places)
Hence, the frequency of the spring is approximately 0.183 Hz.