If my calculations are accurate, the angle is 67.5 degrees.
Displacement stabilizes over time. It is known that exponentials raised to infinity approach zero, hence the system model will yield as time approaches infinity, resulting in 4x'' + e−0.1tx = 0. As time approaches infinity, we deduce that 4x'' equals zero. Consequently, upon integrating, we derive 4x' = c, and further integration leads to the conclusion 4x = cx + d.
Answer:
Maximum emf = 5.32 V
Explanation:
Provided data includes:
Number of turns, N = 10
Radius of loop, r = 3 cm = 0.03 m
It made 60 revolutions each second
Magnetic field, B = 0.5 T
We are tasked to determine the maximum emf produced in the loop, which is founded on Faraday's law. The induced emf can be calculated by:
For the maximum emf, 
Therefore,
Hence, the maximum emf generated in the loop is 5.32 V.
Response: The spring constant is 25 N/m.
Details:
The body’s mass is 25 g, which converts to 0.025 kg (since 1 kg = 1000 g).
The total oscillations are 20 in 4 seconds.
Oscillations per second = 
Spring's frequency of vibration is = 
The spring constant 'k' can be derived from the relationship involving frequency, mass, and spring constant.
The spring constant is 25 N/m.
I will analyze each option. My assumption is that the answer is C.
Option A states that gravity acts downward on the box but does not affect its horizontal acceleration, provided there is no friction.
Option B indicates that the normal force goes upward on the box, which also does not influence horizontal acceleration.
In option C, the reaction force discussed relates to Newton’s 3rd law. This reaction force acts on Lien rather than the box itself, meaning she must overcome this force to set the box in motion. I believe this is the correct choice.
Option D refers to the push force applied by her; she wouldn’t have to counteract her own force regarding the box, but must address the reaction force as I mentioned in option C.
