Answer:
Lenz's law
Explanation:
it states that induced emf of different polarities induces a current whose magnetic field opposes the change in magnetic flux through the coil in order to ensure that original flux is maintained through the coil when current flows in it.
according to Faraday' s law of electromagnetic induction
Where -ve sign due to lenz's law
Emf is the induced voltage also known as electromotive force
N is the number of loops.
dϕ Change in magnetic flux.
dt Change in time.
<span>If your speed changes from 10 km/h to 6 km/h, you have a negative acceleration. The correct option among all the options that are given in the question is the first option or option "a". The other choices are totally incorrect. I hope that this is the answer that has actually come to your help.</span>
Answer:
(a) F = 15.12 N
(b) a = 30.24 m/s²
(c) To Left
Explanation:
(a)
The magnitude of the spring force is given by Hooke's Law as follows:
F = kx
where,
F = Spring Force = ?
k = Spring Constant = 126 N/m
x = Displacement = A = 0.12 m
Therefore,
F = (126 N/m)(0.12 m)
<u>F = 15.12 N</u>
(b)
The magnitude of acceleration can be found by comparing the spring force with the unbalanced force formula of Newton's Second Law:
F = ma
where,
F = Spring Force = 15.12 N
m = mass of block = 0.5 kg
a = magnitude of acceleration = ?
15.12 N = 0.5 kg (a)
a = 15.12 N/0.5 kg
<u>a = 30.24 m/s²</u>
<u></u>
(c)
Since, the acceleration is always directed towards mean (equilibrium) position in periodic motion. Therefore, the direction of the acceleration at the time of release will be <u>to left.</u>
Yp(t) = A1 t^2 + A0 t + B0 t e(4t)
=> y ' = 2A1t + A0 + B0 [e^(4t) +4 te^(4t) ]
y ' = 2A1t + A0 + B0e^(4t) + 4B0 te^(4t)
=> y '' = 2A1 + 4B0e(4t) + 4B0 [ e^(4t) + 4te^(4t)
y '' = 2A1 + 4B0e^(4t) + 4B0e^(4t) + 16B0te^(4t)
Now substitute the values of y ' and y '' in the differential equation:
<span>y′′+αy′+βy=t+e^(4t)
</span> 2A1 + 4B0e^(4t) + 4B0e^(4t) + 16B0te^(4t) + α{2A1t + A0 + B0e^(4t) + 4B0 te^(4t) } + β{A1 t^2 + A0 t + B0 t e(4t)} = t + e^(4t)
Next, we equate coefficients
1) Constant terms of the left side = constant terms of the right side:
2A1+ 2αA0 = 0 ..... eq (1)
2) Coefficients of e^(4t) on both sides
8B0 + αB0 = 1 => B0 (8 + α) = 1 .... eq (2)
3) Coefficients on t
2αA1 + βA0 = 1 .... eq (3)
4) Coefficients on t^2
βA1 = 0 ....eq (4)
given that A1 ≠ 0 => β =0
5) terms on te^(4t)
16B0 + 4αB0 + βB0 = 0 => B0 (16 + 4α + β) = 0 ... eq (5)
Given that B0 ≠ 0 => 16 + 4α + β = 0
Use the value of β = 0 found previously
16 + 4α = 0 => α = - 16 / 4 = - 4.
Answer: α = - 4 and β = 0
