A mass is bobbing up and down on a spring. If you increase the amplitude of the motion, how does this affect the time for one os
1 answer:
Answer:
It will not change
Explanation:
The period of oscillation of a mass-spring system is given by
where
T is the period
m is the mass hanging on the spring
k is the spring constant
As we see from the formula, the period of oscillation does not depend on the amplitude of the motion: therefore, if we change the amplitude, the time for one oscillation will not change.
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Recall the period of an orbit is how long it takes the satellite to make a complete orbit around the earth. Essentially, this is the same as 'time' in the distance = speed * time equation. For an orbit, we can define these quantities:
← The circumference of the orbit
speed = orbital speed, we will solve for this later
time = period
Therefore:
Where 'r' is the orbital radius of the satellite.
First, let's solve for 'v' assuming a uniform orbit using the equation:
G = Gravitational Constant (6.67 × 10⁻¹¹ Nm²/kg²)
m = mass of the earth (5.98 × 10²⁴ kg)
r = radius of orbit (1.276 × 10⁷ m)
Plug in the givens:
Now, we can solve for the period: