Answer:
1. The period is 1.74 s.
2. The frequency is 0.57 Hz
Explanation:
1. Determination of the the period.
Spring constant (K) = 30 N/m
Mass (m) = 2.3 Kg
Pi (π) = 3.14
Period (T) =?
The period of the vibration can be obtained as follow:
T = 2π√(m/K)
T = 2 × 3.14 × √(2.3 / 30)
T = 6.28 × √(2.3 / 30)
T = 1.74 s
Thus, the period of the vibration is 1.74 s.
2. Determination of the frequency.
Period (T) = 1.74 s
Frequency (f) =?
The frequency of the vibration can be obtained as follow:
f = 1/T
f = 1/1.74
f = 0.57 Hz
Thus, the frequency of the vibration is 0.57 Hz
The period of the vibration is 1.76 s and the frequency of the vibration is 0.57 s-1.
Using the formula;
T = 2π√(m/K)
Where;
T = period
m = mass
K = spring constant
Substituting values;
T = 2(3.142)√2.3/30
T = 6.284 × 0.28
T = 1.76 s
Recall that the period is the inverse of frequency;
f = 1/T
f = 1/1.76 s
f = 0.57 s-1
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