g A coil formed by wrapping 50 turns of wire in the shape of a square is positioned in a magnetic field so that the normal to th
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a)
b) See plot attached
c) 10.0 m
d) 0.500 cm
Explanation:
a)
The position of the tip of the lever at time t is described by the equation:
(1)
The generic equation that describes a wave is
(2)
where
A is the amplitude of the wave
T is the period of the wave
t is the time
By comparing (1) and (2), we see that for the wave in this problem we have
Therefore, the period is
b)
The sketch of the profile of the wave until t = 4T is shown in attachment.
A wave is described by a sinusoidal function: in this problem, the wave is described by a sine, therefore at t = 0 the displacement is zero, y = 0.
The wave than periodically repeats itself every period. In this sketch, we draw the wave over 4 periods, so until t = 4T.
The maximum displacement of the wave is given by the value of y when , and from eq(1), we see that this is equal to
y = 0.500 cm
So, this is the maximum displacement represented in the sketch.
c)
When standing waves are produced in a string, the ends of the string act as they are nodes (points with zero displacement): therefore, the wavelength of a wave in a string is equal to twice the length of the string itself:
where
is the wavelength of the wave
L is the length of the string
In this problem,
L = 5.00 m is the length of the string
Therefore, the wavelength is
d)
The amplitude of a wave is the magnitude of the maximum displacement of the wave, measured relative to the equilibrium position.
In this problem, we can easily infer the amplitude of this wave by looking at eq.(1).
And by comparing it with the general equation of a wave:
In fact, the maximum displacement occurs when the sine part is equal to 1, so when
which means that
And therefore in this case,
So, this is the displacement.
Answer:
Time period for Simple pendulum,
Explanation:
The Simple Pendulum
Consider a small bob of mass is tied to extensible string of length
that is fixed to rigid support. The bob is oscillating in the plane about verticle.
Let is the angle made by string with vertical during oscillation.
Vertical component of the force on bob,
Negative sign shows that its opposing the motion of bob.
Taking as very small angle then,
Let is the displacement made by bob from its mean position ,
then,
so, ........(1)
Since, pendulum is in hormonic motion,
as we know,
where is the constant and
.........(2)
From equation (1) and (2)
Since,