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Chapter 7: Problem 1

Give an example of motion that's periodic but not oscillatory.

Short Answer

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An example is the Earth's orbit around the Sun, which is periodic but not oscillatory.

Step by step solution

01

Understanding Motion Types

Motion can be categorized into various types, two of which are periodic motion and oscillatory motion. Periodic motion is motion that repeats itself after a fixed interval of time. Oscillatory motion is a specific type of periodic motion where an object moves back and forth around a central, usually equilibrium position.
02

Identifying Non-Oscillatory Periodic Motion

To identify an example, we need to focus on a type of periodic motion that does not involve oscillation. A common form of non-oscillatory periodic motion is circular motion because an object moves along a circular path, repeating its path over regular intervals, without any back-and-forth or oscillating behavior.
03

Example of Non-Oscillatory Periodic Motion

A typical example of periodic but non-oscillatory motion is the motion of the Earth around the Sun. This motion is periodic as it repeats every year but is not oscillatory since the Earth does not move back-and-forth across a central fixed point.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Oscillatory Motion
Oscillatory motion is a fascinating aspect of physics, where an object repeatedly moves back and forth around a central point. This central point is often an equilibrium position.
Consider a swing at a playground: when you push it, the swing moves to and fro. That's oscillatory motion in action!
It always involves some kind of repetitive movement. The key point is that oscillations require a central position that the object regularly returns to.
  • Common examples include: a pendulum, a vibrating guitar string, or any object experiencing simple harmonic motion, like a mass on a spring.
These oscillations can be described mathematically using functions like sinusoidal equations, which capture the wave-like patterns of movement. Oscillatory motion is crucial in understanding waves and many other phenomena in physics.
Circular Motion
Circular motion is another intriguing type of motion, where objects follow a circular path. Imagine a car going around a race track. It moves in a circle, continually changing its direction as it loops around. The key characteristic is the circular trajectory.
In circular motion, the object doesn't go back and forth. Instead, it maintains a continuous path that eventually repeats, classifying it as periodic but non-oscillatory.
  • This contrasts with oscillatory motion since circular motion does not center around an equilibrium point.
  • It involves constant speed along the circle or could include varying speeds, known as non-uniform circular motion.
In many cases, forces like centripetal force keep objects on their circular paths, highlighting important concepts like angular velocity and rotational dynamics.
Earth's Orbit
One of the most captivating examples of circular motion is Earth's orbit around the Sun. This orbit is a brilliant illustration of periodic motion.
Every 365.25 days, Earth completes its annual journey, making the motion predictable and regular.
While many may confuse it with oscillatory motion due to its repetitive nature, it is distinctly non-oscillatory.
  • Earth's movement is not about going back and forth around a center; instead, it's about constantly following a path in space.
  • The orbit itself isn't a perfect circle, but an ellipse, which is still periodic.
The revolution around the Sun affects seasons, climate, and the calendar, demonstrating the importance of understanding Earth's orbit in daily life.

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Most popular questions from this chapter

A mass-spring system has a period of \(5.00 \mathrm{~s}\). If the spring constant is doubled, the new period is (a) \(3.54 \mathrm{~s}\) (b) \(5.00 \mathrm{~s}\) (c) \(7.07 \mathrm{~s}\) (d) \(10.0 \mathrm{~s}\).

A tightrope walker of mass \(m\) stands at rest midway along a cable of length \(L\) and negligible mass. The cable is stretched tightly between two supports, giving it a tension \(F\). If this equilibrium is disturbed, the tightrope walker undergoes smallamplitude vertical oscillations. Show that the period of these oscillations is \(T=2 \pi \sqrt{\frac{m L}{4 F}}\).

A spring \((k=65.0 \mathrm{~N} / \mathrm{m})\) hangs vertically with its top end fixed. A mass attached to the bottom of the spring then displaces it \(0.250 \mathrm{~m}\), establishing a new equilibrium. If the mass is further displaced and then released, what's the period of the resulting oscillations?

A simple harmonic oscillator has \(m=1.50 \mathrm{~kg}, k=80.0 \mathrm{~N} / \mathrm{m}\) and damping parameter \(b=2.65 \mathrm{~kg} / \mathrm{s} .\) Is the motion lightly damped, critically damped, or heavily damped?

Find the total mechanical energy of a mass-spring system with \(m=1.24 \mathrm{~kg}\) and maximum speed \(0.670 \mathrm{~m} / \mathrm{s}\).
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