a) An object with mass m is attached to a spring with spring constant 1 N/m. If the mass is pulled 1m beyond its equilibrium position and given velocity 1 m/s back towards its equilibrium position, this results in an oscillation with amplitude 3 m. i. Determine the equation of motion in the form of x = A sin(?t + Ø). ii. Find the mass m.
Added by Teresa V.
Close
Step 1
37^\circ) \) with an amplitude of 3 m. Show more…
Show all steps
Your feedback will help us improve your experience
Supratim Pal and 79 other Calculus 1 / AB 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
If a mass that is attached to a spring is raised $y_{0}$ feet and released with an initial vertical velocity of $v_{0}$ ft/sec, then the subsequent position $y$ of the mass is given by $$y=y_{0} \cos \omega t+\frac{V_{0}}{\omega} \sin \omega t$$ where $t$ is time in seconds and $\omega$ is a positive constant. (a) If $\omega=1, y_{0}=2 \mathrm{ft},$ and $v_{0}=3 \mathrm{ft} / \mathrm{sec},$ express $y$ in the form $A \cos (B t-C),$ and find the amplitude and period of the resulting motion. (b) Determine the times when $y=0-$ that is, the times when the mass passes through the equilibrium position.
Analytic Trigonometry
The Addition and Subtraction Formulas
A mass m attached to a horizontal massless spring with spring constant k, is set into simple harmonic motion. its maximum displacement from its equilibrium position is a. what is the masses speed as it passes through its equilibrium position?
Prabhat T.
A horizontal spring is set up like the one in Fig. $11-3 .$ It has an elastic constant of $80.0 \mathrm{~N} / \mathrm{m}$. A $2.00$ -kg mass, sitting on a frictionless horizontal surface, is attached to the end of the spring. The mass is displaced $20.0 \mathrm{~cm}$ to the right and released, whereupon it oscillates in SHM. Determine its acceleration (magnitude and direction) and its velocity (magnitude and direction) at its equilibrium position. [Hint: $x=0 .]$
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD