P6 Giancoli 4th Ed
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
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