A sinusoidal graph of position versus time for a weight on a string undergoing simple harmonic motion is provided. The vertical axis is labeled $X$ ($\text{m}$) and the horizontal axis is labeled $t$ ($\text{s}$). The origin is at the intersection of the axes. Tick marks on the time axis are at $0.10\,\text{s}$, $0.30\,\text{s}$, $0.50\,\text{s}$, and $0.70\,\text{s}$. The peak displacement on the vertical axis is $0.15\,\text{m}$ above zero and $-0.15\,\text{m}$ below zero. The sine curve starts at the origin at $t = 0$, reaches a positive maximum near $t = 0.10\,\text{s}$, crosses zero at $t = 0.20\,\text{s}$, reaches a negative minimum near $t = 0.30\,\text{s}$, and continues periodically. Using this graph, answer the following.

Question

A sinusoidal graph of position versus time for a weight on a string undergoing simple harmonic motion is provided. The vertical axis is labeled $X$ ($\text{m}$) and the horizontal axis is labeled $t$ ($\text{s}$). The origin is at the intersection of the axes. Tick marks on the time axis are at $0.10\,\text{s}$, $0.30\,\text{s}$, $0.50\,\text{s}$, and $0.70\,\text{s}$. The peak displacement on the vertical axis is $0.15\,\text{m}$ above zero and $-0.15\,\text{m}$ below zero. The sine curve starts at the origin at $t = 0$, reaches a positive maximum near $t = 0.10\,\text{s}$, crosses zero at $t = 0.20\,\text{s}$, reaches a negative minimum near $t = 0.30\,\text{s}$, and continues periodically. Using this graph, answer the following.(a) Determine the amplitude of the motion from the graph.
, (b) Determine the period of the motion from the graph.
, (c) Calculate the frequency of the motion.
, (d) On the graph, label a point where the velocity is zero.
, (e) On the graph, label the points where the acceleration is maximum and where it is minimum.
, (f) On the graph, indicate the points where the kinetic energy reaches its maximum value.
, (g) On the graph, indicate the points where the potential energy is greatest.
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Jason · Accepted Answer

$A = 0.15\,\text{m}$
$T = 0.40\,\text{s}$
$f = 2.5\,\text{Hz}$
$v = 0 \text{ at } t = 0.10\,\text{s} \text{ and } 0.30\,\text{s}$
$a_{\max} \text{ at } t = 0.30\,\text{s};\; a_{\min} \text{ at } t = 0.10\,\text{s}$
$KE_{\max} \text{ at } t = 0, 0.20\,\text{s}, 0.40\,\text{s}, 0.60\,\text{s}$
$PE_{\max} \text{ at } t = 0.10\,\text{s}, 0.30\,\text{s}, 0.50\,\text{s}$

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