A Mass on a Smooth Tabletop Is Attached to a Spring

question 25

Multiple Choice

A mass on a smooth tabletop is attached to a spring, as shown in the figure. The coordinate system has been chosen so that the equilibrium position of the mass corresponds to $$s = 0$$ . Assume that the simple harmonic motion is described by the equation $$s = 5 \cos \left( \frac { \pi t } { 3 } \right)$$ , where s is in centimeters and t is in seconds. Determine which table describes the s-coordinate of the mass at each of the following times: $$t =$$ 0 sec, 0.5 sec, 1 sec, and 2 sec. (One of these coordinates will involve a radical sign; for this case, use a calculator and round the final answer to two decimal places.)

• A) \[\begin{array} { | c | c | } \hline \text { time (sec) } & \text { s-coordinate(cm) } \\ \hline 0 & 5 \\ \hline 0.5 & 4.33 \\ \hline 1 & 2.5 \\ \hline 2 & 2.5 \\ \hline \end{array}\]
• B) \[\begin{array} { | c | c | } \hline \text { time (sec) } & \text { s-coordinate(cm) } \\ \hline 0 & - 2.5 \\ \hline 0.5 & 4.33 \\ \hline 1 & 2.5 \\ \hline 2 & 5 \\ \hline \end{array}\]
• C) \[\begin{array} { | c | c | } \hline \text { time (sec) } & \text { s-coordinate(cm) } \\ \hline 0 & 5 \\ \hline 0.5 & 4.33 \\ \hline 1 & 2.5 \\ \hline 2 & - 2.5 \\ \hline \end{array}\]
• D) \[\begin{array} { | c | c | } \hline \text { time (sec) } & \text { s-coordinate(cm) } \\ \hline 0 & 2.5 \\ \hline 0.5 & 4.33 \\ \hline 1 & 5 \\ \hline 2 & - 2.5 \\ \hline \end{array}\]
• E) \[\begin{array} { | c | c | } \hline \text { time (sec) } & \text { s-coordinate(cm) } \\ \hline 0 & 5 \\ \hline 0.5 & 2.5 \\ \hline 1 & 4.33 \\ \hline 2 & - 2.5 \\ \hline \end{array}\]

---

Definitions:

Optogenetics

Transgenic technique that combines genetics and light to excite or inhibit targeted cells in living tissue.

Blue Light

A high-energy, short-wavelength light that is emitted by electronics screens and can affect sleep and eye health.

Green-Yellow Light

A range of light wavelengths perceived by the human eye as between green and yellow, often associated with specific visual or physiological effects.

Deep Brain Stimulation

A neurosurgical procedure involving the implantation of a medical device called a neurostimulator, which sends electrical impulses to specific targets in the brain for the treatment of movement and neuropsychiatric disorders.