Answer:
The natural angular frequency of the rod is 53.56 rad/sec
Explanation:
Since the beam is free at one end and fixed at the other hence the beam is a cantilevered beam as shown in the attached figure
We know that when a unit force is placed at the end of a cantilever the displacement of the free end is given by
Hence we can write
Comparing with the standard spring equation 
we find the cantilever analogous to spring with 
Now the angular frequency of a spring is given by
where
'm' is the mass of the load
Thus applying values we get
The maximum Speed of the Sprinter from the velocity time graph of his motion is; 11.98 m/s
<h3>How to find the maximum speed?</h3>
We are given;
Initial Speed; u = 2.5 s
Total distance; d = 100 m
Total time; T = 9.6 s
The total distance is;
d = ¹/₂(9.6 + (9.6 - 2.5) * v
where v is maximum speed.
Thus;
¹/₂(9.6 + (9.6 - 2.5) * v = 100
16.7v = 200
v = 200/16.7
v = 11.98 m/s
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Answer:
L = Henry
C = Farad
Explanation:
The electrical parameter represented as L is the inductance whose unit is Henry(H).
The electrical parameter represented as C is the inductance whose unit is Farad
Resonance frequency occurs when the applied period force is equal to the natural frequency of the system upon which the force acts :
To obtain :
At resonance, Inductive reactance = capacitive reactance
Equate the inductive and capacitive reactance
Inductive reactance(Xl) = 2πFL
Capacitive Reactance(Xc) = 1/2πFC
Inductive reactance(Xl) = Capacitive Reactance(Xc)
2πFL = 1/2πFC
Multiplying both sides by F
F * 2πFL = F * 1/2πFC
2πF²L = 1/2πC
Isolating F²
F² = 1/2πC2πL
F² = 1/4π²LC
Take the square root of both sides to make F the subject
F = √1 / √4π²LC
F = 1 /2π√LC
Hence, the proof.
Answer:
Coiled tubing is often used to carry out operations similar to wire lining.
