A mass of 0.407 kilograms is oscillating horizontally on a spring. Its position is given by the equation x = [0.108 sin (9.24t+ 0.82) + 0.683] m. a. What is the spring constant of the spring? Include units in your answer. More information. b. The velocity of the mass is another sinusoid, which also can be modeled using the equation v = [A sin (Bt + C) + D] m/s. What are those values? Do not bother with units. 40 B: M C: ✓ D: c. The acceleration of the mass is yet another sinusoid, which again can be modeled using the equation a= [A sin (Bt + C) + D] m/s/s. What are those values of A and C? Do not bother with unit Hint: For A, consider Newton's second law of motion. A: 4.0 C: 40 (between 0 and 2) (between 0 and 2x) Note that the values of B and D for the acceleration equation are the same as the values of B and D for the velocity equation.
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
A mass of 0.407 kilograms is oscillating horizontally on a spring. Its position is given by the equation x = [0.108 sin (9.24t + 0.82) + 0.683] m.
a. What is the spring constant of the spring? Include units in your answer. More information.
b. The velocity of the mass is another sinusoid, which also can be modeled using the equation v = [A sin (Bt + C) + D] m/s. What are those values? Do not bother with units.
A:
B:
C: (between 0 and 2?)
D:
c. The acceleration of the mass is yet another sinusoid, which again can be modeled using the equation a = [A sin (Bt + C) + D] m/s/s. What are those values of A and C? Do not bother with units. Hint: For A, consider Newton's second law of motion.
A:
C: (between 0 and 2?)
Note that the values of B and D for the acceleration equation are the same as the values of B and D for the velocity equation.
![A mass of 0.407 kilograms is oscillating horizontally on a spring. Its position is given by the equation x = [0.108 sin (9.24t + 0.82) + 0.683] m.
a. What is the spring constant of the spring? Include units in your answer. More information.
4.0
b. The velocity of the mass is another sinusoid, which also can be modeled using the equation v = [A sin (Bt + C) + D] m/s. What are those values? Do not bother with units.
A: 4.0
B: 4.0
C: 4.0
D:
c. The acceleration of the mass is yet another sinusoid, which again can be modeled using the equation a = [A sin (Bt + C) + D] m/s/s. What are those values of A and C? Do not bother with units.
Hint: For A, consider Newton's second law of motion.
(between 0 and 2π)
A: 4.0
C: 4.0
(between 0 and 2π)
Note that the values of B and D for the acceleration equation are the same as the values of B and D for the velocity equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf449e0d-066d-4e9d-b973-521625ba6ff9%2F93385940-6d0f-4fd3-b9bd-c04516316726%2Flmsoh3r_processed.png&w=3840&q=75)
(a) The equation for the position of the mass on the spring is given by:
x = 0.108 sin(9.24t + 0.82) + 0.683
Comparing this to the standard equation for simple harmonic motion:
x = A sin(ωt + φ)
where A is the amplitude, ω is the angular frequency, and φ is the phase angle, we can see that:
A = 0.108 m ω = 9.24 rad/s
The spring constant, k, is related to the angular frequency by the equation:
ω = sqrt(k/m)
where m is the mass of the object on the spring. Rearranging this equation gives:
k = mω^2
Substituting in the values for m and ω gives:
k = (0.407 kg)(9.24 rad/s)^2 ≈ 14.9 N/m
Therefore, the spring constant of the spring is approximately 14.9 N/m.
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