What is the power p supplied to a resistor whose resistance is r when it is known that it has a voltage δv across it?
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Answer:
0·149 s
Explanation:
Initially at t = 0 s, velocity of the block = v = 2 m/s and = - 0·33 m from the equilibrium position of the spring
Spring constant k = 61·2 N/m
Acceleration of the block at any instant of time = - (k × x) ÷ m
<h3>As acceleration of the block depends on x and acts in opposite direction to the motion of the block</h3><h3>The motion of the block will be simple harmonic motion</h3><h3>Then the equation of motion = x = A × sin(w × t + c)</h3>Where x is the distance of the block from equilibrium position
A is the amplitude( that is maximum distance from the equilibrium position)
w is the angular frequency
t is the time taken
c is any constant
<h3>For simple harmonic motion a = - w² × x</h3>- w² × x = - (k × x) ÷ m
From the above equation w = √(k ÷ m) = √(61·2 ÷ 5) = 3·499 rad/s
By substituting the values in the given equation
- 0·33 = A × sin(c) → equation 1
By differentiating the equation x = A × sin(w × t + c) with respect to t on both sides
v = A × w × cos(w × t + c)
By substituting the values
2 = A × w × cos(c) → equation 2
By dividing the equation 1 and equation 2
- (0·33 ÷ 2) × w = tan(c)
tan(c) = - 0·577
⇒ c = π - inverse of tan(0·577)
∴ c = π - 0·523 rad
Substituting the value of c in equation 1
- 0·33 = A × sin(π - 0·523)
∴ A = - 36·67 m
∴ x = - 36·67 × sin(3·499 × t + π - 0·523)
At x = 0
sin(3·499 × t + π - 0·523) = 0
∴ 3·499 × t + π - 0·523 = 0 or π
It can't be 0 because if it is 0, then t is negative
∴ 3·499 × t + π - 0·523 = π
3·499 × t = 0·523
∴ t = 0·523 ÷ 3·499 = 0·149 s
∴ Here = 0·149 s