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Chapter 3: Problem 52

An object moves to and fro produces oscillatory motion. If the object moves to and fro at faster rate, it is called vibratory motion.

Short Answer

Expert verified
Answer: The key differences between oscillatory motion and vibratory motion are: 1) vibratory motion is faster than oscillatory motion, and 2) vibratory motion usually involves smaller displacements from the equilibrium position compared to oscillatory motion. They are related in the sense that vibratory motion is a subtype of oscillatory motion, as both involve an object moving back and forth around an equilibrium position. Every vibratory motion is also an oscillatory motion, but not every oscillatory motion is vibratory.

Step by step solution

01

Understand Oscillatory Motion

Oscillatory motion is a type of motion where an object moves back and forth from its equilibrium position, such as a swinging pendulum or a mass attached to a spring. In this type of motion, the object moves in a periodic manner and its displacement from the equilibrium position varies sinusoidally with time.
02

Understand Vibratory Motion

Vibratory motion is a subtype of oscillatory motion. Like oscillatory motion, an object in vibratory motion moves back and forth from its equilibrium position. The key difference is that vibratory motion occurs at a faster rate and usually involves smaller displacements from the equilibrium position. This behavior is commonly observed in musical instruments, such as vibrating strings or tuning forks.
03

Compare Oscillatory and Vibratory Motion

Comparing these two types of motion, we can notice the following differences: 1. Rate: Vibratory motion is faster than oscillatory motion. 2. Displacement: Vibratory motion typically involves smaller displacements from the equilibrium position compared to oscillatory motion.
04

Investigate the Connection between Oscillatory and Vibratory Motion

Although oscillatory and vibratory motions have their differences, they are very closely-related. In fact, vibratory motion can be considered a subtype of oscillatory motion, as both types involve an object moving back and forth around an equilibrium position. So, every vibratory motion is also an oscillatory motion, but not every oscillatory motion is vibratory. Vibratory motion is specifically characterized by the fast rates and small displacements. With this understanding of oscillatory motion and vibratory motion, the given exercise has been broken down into concepts, their differences and connections to have a clear vision of these motion types.

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Most popular questions from this chapter

The speed and average speed of the vehicle can be equal if the vehicle moves with uniform speed or constant speed.

The rate of change of velocity is acceleration.

Fill in the Blanks. vibratory The molecules in solid undergo vibratory motion.

\(1 \mathrm{~km} \mathrm{~h}^{-1}=10^{3} \mathrm{~m} \times \mathrm{h}^{-1}\) \(=\frac{1000 \mathrm{~m}}{1 \mathrm{~h}}=\frac{1000 \mathrm{~m}}{60 \times 60 \mathrm{~s}}\) \(=\frac{10}{36} \mathrm{~m} \mathrm{~s}^{-1}=\frac{5}{18} \mathrm{~m} \mathrm{~s}^{-1}\)

Consider a body moving with initial velocity u. Let its velocity change to \(\mathrm{v}\), in time ' \(\mathrm{t}^{\prime}\). Then, the change in velocity is \(=\mathrm{v}-\mathrm{u}\). The change in velocity per unit time \(=\frac{\mathrm{v}-\mathrm{u}}{\mathrm{t}}\) By definition, the change in velocity per unit time is acceleration, a. Thus, \(\mathrm{a}=\frac{\mathrm{v}-\mathrm{u}}{\mathrm{t}}\) or \(\mathrm{v}-\mathrm{u}=\) at \(\mathrm{v}=\mathrm{u}+\mathrm{at}\)
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