The question asks for the smallest interval of time after which a periodic motion repeats itself. This is a fundamental definition in the study of oscillations and waves.
Correct Option: D) Period — The period (\(T\)) of a periodic motion is defined as the smallest interval of time after which the motion exactly repeats itself. For instance, a pendulum completes one full swing (back and forth) in one period.
The question asks for the SI unit of frequency. We need to recall the definition of frequency and its standard unit in the International System of Units (SI).
C) Hertz (Hz) is the correct SI unit for frequency. One Hertz is equivalent to one cycle per second (\(1 \text{ Hz} = 1 \text{ s}^{-1}\)).
This question asks to find the frequency of a pendulum given its time period. The relationship between time period and frequency is fundamental in physics, especially in the study of oscillations and waves. Frequency is the reciprocal of the time period.
The frequency and time period are inversely proportional to each other. The formula connecting them is:
\[ f = \frac{1}{T} \]The time period of the pendulum is given as \(T = 0.5\) seconds.
Substitute the given time period into the formula:
\[ f = \frac{1}{0.5 \text{ s}} \]\[ f = \frac{1}{\frac{1}{2} \text{ s}} \]\[ f = 2 \text{ Hz} \]Correct Option: D) 2 Hz
The problem asks us to calculate the frequency of a human heart given its beat rate. Frequency is defined as the number of cycles or events per unit of time. In this case, the events are heartbeats, and the unit of time is typically seconds for frequency (measured in Hertz, Hz).
Correct Option: C) 1.25 Hz
To answer this question, we need to understand the definitions of periodic motion and oscillatory motion and the relationship between them. We will analyze each option based on these definitions.
D) Every oscillatory motion is periodic, but every periodic motion need not be oscillatory. This statement correctly captures the relationship between the two types of motion. Oscillatory motion is a specific type of periodic motion where the movement is back and forth about a mean position. All such back-and-forth movements are inherently repetitive and thus periodic. However, periodic motions like uniform circular motion are repetitive but do not involve oscillation.
To understand the difference between vibration and oscillation, it's important to define both terms and identify their key characteristics. Both refer to repetitive motions, but the context and typical frequency range distinguish them.
Correct Option: D) Frequency
Vibration is essentially an oscillation that occurs at a relatively high frequency. The terms are often used interchangeably, but when a distinction is made, frequency is the primary differentiating factor.