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 of the weight has a mass of .4 kilogram.
To find the period of the spring, we need to identify the value of the frequency first.
The equation for the vertical displacement is given as y = 1.5cos(√(kt/m)).
Comparing this with the general equation for simple harmonic motion (SHM), y = Acos(ωt), we can see that ω represents the angular frequency, and it is related to the frequency (f) and the period (T) as follows:
ω = 2πf = (2π)/T.
From the given equation, we can deduce that √(kt/m) = ω.
Since k (elasticity coefficient) is given as 18.5 and m (mass) is given as 0.4 kg, we can insert these values into the equation to calculate ω.
√(kt/m) = ω
√(18.5t/0.4) = ω
√(46.25t) = ω.
Now, we have the relationship √(46.25t) = ω.
To find the period (T), we can use the equation T = (2π)/ω.
Substituting the value of ω obtained previously:
T = (2π)/√(46.25t).
Now, we can plug in the mass (m = 0.4 kg) to calculate the period (T):
T = (2π)/√(46.25 * 0.4).
After evaluating this expression, you will obtain the period of the spring for a weight of 0.4 kg. To find the frequency (f), you can use the equation f = 1/T, where T is the period you obtained.
Please note that you will need to use an appropriate calculator to perform these calculations accurately.