Question

Is the force due to gravity the only restoring force in problem #1 of the attached image?

Answer 1

There's 2 forces at play here, gravity being the more interesting one. But there's also the force of tension on the line that cancels the component of the gravitational force that is parallel to radius vector leaving just the force that drives the pendulum left-right.

There seems to be drawn a force of 60N, I assume it's drawn there to represent the net force after you cancel the tension and gravity components, but if it's some other outside force, such as the ones you can have under force-driven oscillations, then you've got to add that to the list. But as I said, this doesn't appear to be the case from the question context.

I'd answer yes.

Answer 2

I think the 60N force is an external force.

Answer 3

Easy way to check would probably be to solve the problem, if you get that at 30° the force at the end of the stick is 60N then it probably isn't an external force. Do pay attention though because it's a solid stick with quite a bit of mass so presumably moment of inertia comes into play. The trick here is to take the moment of inertia of a rod, but the radius at halfway point, but you can also take the parallel axis theorem to get the moment of inertia on its ends: http://hyperphysics.phy-astr.gsu.edu/hbase/parax.html#pax

In any case the question then has no real meaning, if there's an outside force acting on the pendulum/rod, then there's no way to answer where does the restoring force come from, since it could be a motor, a spring, someone's hand etc....

Answer 4

If my jaded memory serves me, this is an "un simple" pendulum, because the "string" is a piece of metal, and has mass. I'm hesitating on calling it a "compound pendulum", because I think that that is when there's another mass connected to the first mass and hanging down.
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Answer 5

Is the force due to gravity the only restoring force in problem #1 of the attached image? To answer your question specifically, I would say no, it isn't. The question shows a 60N force which I think serves as another restoring force.
It's as though you'd taken the bob/mass of a SIMPLE -string - pendulum, pulled it aside and then rather than just letting it go, you'd PUSHED it. If you just released it, then the pendulum would swing back and forth in SIMPLE HARMONIC MOTION, SHM. If you PUSH it, then, you put an extra force in there, and it wouldn't be SHM.
A loose analogy here may be a playground swing. The swing would do DAMPED harmonic motion if you pulled the seat aside, and then just released it and let the thing swing to and fro. However, the person on the seat would get bored. So, you tend to catch the swing when it comes back, and give it another push. The person then goes "yipppeee". If you pushed with a big enough force, of course, there's a chance that the seat could to over the top of the support and, well, disaster basically.
I've had a look at the questions in your attachment and I wonder ...
Answers due in next friday ... how long have you had the questions for ?
It looks like it's an APPLIED MATHS homework - that's what I'd call it in UK. The marks seem to be pretty mean in comparison to the volume of numbers in the questions.
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Answer 6

gravity is the restoring force here