Answer:
(a) A = 0.700m
(b) k = 80.6N/m
(c) x = -0.699m
(d) x = -0.350m
(e) t = 0.168s
Explanation:
Given the equation of motion for the spring
X = 0.700cos(12.0t), m = 0.56kg
(a) A = amplitude = 0.700m
(b) The angular velocity ω = 12rad/s
ω = √(k/m)
ω² = k/m
k = m×ω² = 0.56×12² = 80.6N/m
Spring constant k = 80.6N/m
(c) T = 2π/ω = 2π/12
T = 0.524s
At t = T/2 = 0.524/2 = 0.262s
So x = 0.700cos(12×0.262) = –0.699m
(d) At t = 2/3×T = 2×0.524/3 = 0. 349s
x = 0.700cos(12×0.349) = –0.350m
(e) to find t at x = -0.300m
–0.300 = 0.700cos(12t)
–0.300/0.700 = cos(12t)
cos(12t) = –0.429
12t = cos-¹(-0.429)
12t = 2.01
t = 2.01/12
t = 0.168s
Answer:
The magnitude of the current is 5.45 mA.
Explanation:
Given that,
Resistance = 10.0 ohm
Radius = 0.10 m
Magnetic field = 1.0 T
Angle = 30°
Increase magnetic field = 7.0 T
Time t = 3.0 s
Number of turns = 1
We need to calculate the initial flux
Using formula of flux

Put the value into the formula



We need to calculate the final flux


We need to calculate the induced emf
Using formula of emf

Put the value into the formula


We need to calculate the current
Using formula of current

Put the value into the formula


Hence, The magnitude of the current is 5.45 mA.
The volume of the gas is 
Explanation:
At standard temperature and pressure (stp), the volume occupied by 1 mole of an ideal gas is always equal to

In this problem, we have an amount of moles of gas of
n = 0.034 mol
Since 1 mol of gas occupies a volume of 22.4 L, we can set up the following ratio:

where V is the volume occupied by 0.034 mol of gas. Solving for V, we find

Or, in cubic metres,

Learn more about ideal gases:
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Answer:
4 longitudinal waves
Explanation:
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