A simple harmonic oscillator oscillates with frequency f when its amplitude is
1 answer:
If the amplitude is doubled, the frequency is still f.
In fact, the frequency of a simple harmonic oscillator does not depend on the amplitude. The frequency of the oscillator in fact is:
where
k is the spring constant
m is the mass attached to the spring
We can see that the frequency does not depend on the amplitude A, but only on the properties of the oscillator, so if the amplitude is doubled, the frequency does not change.
In fact, the frequency of a simple harmonic oscillator does not depend on the amplitude. The frequency of the oscillator in fact is:
where
k is the spring constant
m is the mass attached to the spring
We can see that the frequency does not depend on the amplitude A, but only on the properties of the oscillator, so if the amplitude is doubled, the frequency does not change.
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Answer:
a) 29062.125 N·m
b) 0 N·m
c)
d) T = 11186.02 N
Explanation:
We are given
Beam mass = 1975 kg
Beam length = 3 m
Cable angle = 60° above horizontal
a) We have the formula for torque given as follows;
Torque about the pin = Force × Perpendicular distance of force from pin
Where the force = Force due to gravity or weight, we have
Weight = Mass × Acceleration due to gravity = 1975 × 9.81 = 19374.75 N
Point of action of force = Midpoint for a uniform beam = length/2
∴ Point of action of force = 3/2 = 1.5 m
Torque due to gravity = 19374.75 N × 1.5 m = 29062.125 N·m
b) Torque about the pinned end due to the contact forces between the pin and the beam is given by the following relation;
Since the distance from pin to the contact forces between the pin and the beam is 0, the torque which is force multiplied by perpendicular distance is also 0 N·m
c) To find the expression for the tension force, T we find the sum of the moment forces about the pin as follows
Sum of moments about p is given as follows
∑M = 0 gives;
T·sin(θ) × L= M×L/2×g
Therefore torque due to tension is given by the following expression
d) Plugging in the values in the torque due to tension equation, we have;
Therefore, we make the tension force, T the subject of the formula hence