Answer:
x = 0.40 m
Explanation:
- When the displacement is maximum, the particle is momentarily at rest, which means that at this point (assuming no friction present) all the mechanical energy is elastic potential, which can be written as follows:
- Since in absence of friction, total mechanical energy must keep constant, this means that at any time, the sum of the kinetic and potential energy, must be equal to (1), as follows:
- If KEf = U/2f, replacing in (2), we get:
- At any point, the elastic potential energy is given by the following expression:
where k= spring constant (N/m) and x is the displacement from the
equilibrium position.
- Replacing (4) in (3), simplifying and rearranging, we get:
- Finally, solving for x, we get:
A change of colour, heat being released or fizzing (a gas being released)
Capacitor in series with a 100Ω resistor and a 18.0 mH inductor will give a resonance frequency of 1000 Hz is 1.38F
Resonance Frequency of a combination of Series LCR circuit is the frequency at which resonance is achieved in a circuit.
Resonance Frequency of a combination of Series LCR circuit is given by:
f = 1 / 2π
where, f is the resonance Resonance Frequency of a combination of Series LCR circuit
L is the Inductance of the inductor
C is the capacitance of the capacitor
Given,
f = 1000Hz
L = 18.0 mH = 0.018H
R = 100Ω
C = ?
On substituting the values in the above-mentioned formula:
1000 = 1 / 2π
2π = 0.001
On solving, C = 1.38 F
Hence, the capacitance of the given capacitor is 1.38F.
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KE = 10 joules
ke = 1/2 x 0.8 x 5 x v2