The period of the function \begin{equation*} x(t) = \sin(2\pi t) \end{equation*}
Added by Marc T.
Close
Step 1
The angular frequency, ω, is the coefficient of t in the function, which in this case is 2Ï€. The period, T, is the time it takes for the function to complete one full cycle. The formula for the period is T = 2Ï€/ω. Substituting ω = 2Ï€, we get T = Show more…
Show all steps
Your feedback will help us improve your experience
Dominique Jan Tan and 80 other Physics 102 Electricity and Magnetism educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The time average of some function $f(t)$ taken over an interval $T$ is given by $$\langle f(t)\rangle_{\mathrm{T}}=\frac{1}{T} \int_{t}^{t+T} f\left(t^{\prime}\right) d t^{\prime}$$ where $t^{\prime}$ is just a dummy variable. If $\tau=2 \pi / \omega$ is the period of a harmonic function, show that $\overrightarrow{\mathbf{r}}$$$\begin{array}{l}\left\langle\sin ^{2}(\overrightarrow{\mathbf{k}} \cdot \overrightarrow{\mathbf{r}}-\omega t)\right\rangle=\frac{1}{2} \\\left\langle\cos ^{2}(\overrightarrow{\mathbf{k}} \cdot \overrightarrow{\mathbf{r}}-\omega t)\right\rangle=\frac{1}{2}\end{array}$$ and$$\langle\sin (\overrightarrow{\mathbf{k}} \cdot \overrightarrow{\mathbf{r}}-\omega t) \cos (\overrightarrow{\mathbf{k}} \cdot \overrightarrow{\mathbf{r}}\omega t)\rangle=0$$when $T=\tau$ and when $T>>\tau$.
The function $\sin ^{2}(\omega t)$ represents $\quad$ (a) a simple harmonic motion with a period $\pi / \omega$ (b) a simple harmonic motion with a period $2 \pi / \omega$ (c) a periodic with a period $\frac{\pi}{3}$, but not simple harmonic motion (d) a periodic with a period $\frac{2 \pi}{3}$, but not simple harmonic motion
Oscillations
Round 2
What are the period $P$ and frequency $T$ of oscillation of a pendulum of length $\frac{1}{2} \mathrm{ft} ?(\text { Hint: } P=2 \pi \sqrt{\frac{L}{32}}$ where $L$ is the length of the pendulum in feet and the period $P$ is in seconds.)
The Circular Functions and Their Graphs
Harmonic Motion
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD
