P6 Giancoli 4th Ed

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Give some example of everyday vibrating object. which exhibit SHM, at least approximately? 1. The pendulum on an old clock.
2. A guitar string after it gets plucked
3. The vibrations of the little quartz crystal in a digital watch. 2. toys called Newton's cradle
3. the motion of a piston in an engine and
4. the vibrations of the atoms in a solid.
5. A micromass particle of light exhibits SHM.The Reason is that it oscillates without any mass changes during its motion. Is the acceleration of a simple harmonic oscillator ever zero? If so, when? What about a damped harmonic?

Yes. At the point in the center, the acceleration drops to zero and changes direction when the velocity changes from increasing to decreasing. The acceleration is zero as it crosses the equilibrium point. Yes; the acceleration is zero when the velocity is at its maximum, that is, at the equilibrium position. Since the force and hence the acceleration always act TOWARDS the equilibrium position (because it's a restorative force), then the force and acceleration must change their sign as the mass crosses the e.p., and therefore must be zero instantaneously at the e.p.

Why is the motion of a piston in an automobile engine approximately simple harmonic?

If a pendulum clock is accurate at sea level, will it gain or lose time when taken to high altitude? Why? A pendulum clock works using gravity. Gravity pulls the mass towards the equilibrium position at the bottom. Suppose your high altitude results in gravity being 1/10 what it was at sea level. Using F=ma, we see that the force due to gravity is smaller, mass is constant, so acceleration must decrease. Since the pendulum cannot accelerate as quickly, it cannot reach the maxima on either side of the equilibrium as quickly, resulting in a loss of time. (The clock runs slower) It will gain time.

Higher Altitude = Less Gravitational Force

Less Gravitational Force = Less Force on the Fabric of Time

Clocks go faster with less resistance.

Albeit, the difference will be minute, but there will be a difference It will lose time.. but only very slightly. Pendulum clocks keep constant time only when the accelerative force on the pendulum due to gravity remains constant. As the distance between the centers of the two masses (the earth and the pendulum) increases, the accelerative force due to gravity decreases, thus slowing the movement of the pendulum and the clock in turn.

the period of a simple pendulum at low ampltitude is:
T = 2 pi sqrt (l/g)

As you go up, g goes down, so it RUNS SLOW. :)
Since the acceleration due to gravity decreases, the frequency will also decrease which means the angular frequency will decrease so it will lose time. I also think that the pendulum clock will lose time because the acceleration due to gravity is decreasing and it is moving away from the center. I agree the clock will lose time at a higher altitude.

I also agree and think that the pendulum clock will lose time... this is because the acceleration due to gravity decreases so the the frequency will also decrease causing the angular frequency to decrease I think that the clock will lose time also because since the acceleration due to gravity decreases as you move up in altitude the frequency will decrease as well resulting in a lose of time I also that the clock would lose time because since the force due to gravity decreses, the pendulum feels less of a pull downward so it would sway slower. The clock will lose time as it increases in altitude. As you increase in altitude, the force of gravity increases. Therefore, as the clock is taken to a higher altitude, the force of gravity on the pendulum will increase, and will decrease the time. An increase in altitude would cause the pendulum clock to slow losing time. At the higher altitude the force of gravity will decrese the acceleration. The acceleration of gravity at sea level is at its maximum and any variance from that point (above sea...
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