A student records both the displacement–time and acceleration–time graphs for a mass…

PHYSICS · Multi-part · CBSE · Physics · Oscillations · Oscillations

Problem

A student records both the displacement–time and acceleration–time graphs for a mass oscillating on a spring. The following measured values are obtained from the two graphs. • Maximum displacement:

x_{\text{max}} = 0.10\,\text{m}

• Maximum magnitude of acceleration:

a_{\text{max}} = 3.9\,\text{m\,s}^{-2}

• Period of the motion:

T = 0.70\,\text{s}

• The acceleration graph reaches its negative maximum at

t = 0

. The displacement graph reaches its positive maximum at

t = 0.045\,\text{s}

. The student wishes to verify that the motion is consistent with simple harmonic motion. (a) Using the numerical data, calculate the theoretical value of

a_{\text{max}}

predicted from

x_{\text{max}}

and the measured period. Show all steps. (b) Determine the phase constant (in radians) that relates the displacement and acceleration graphs, based on the measured

0.045\,\text{s}

time shift. State whether this phase constant is consistent with ideal simple harmonic motion. (c) Predict the sign (positive, negative, or zero) and approximate magnitude of the velocity at

t = 0.045\,\text{s}

. Justify your prediction without explicitly plotting a velocity graph. (d) If the calculated and measured

a_{\text{max}}

values differ by more than

10\%

, provide one plausible experimental source of error and describe how it would affect the graphs.

Related theory

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