Questions: The position of a 50 g oscillating mass is given by x(t)=(2.0 cm) cos (10 t-π / 4), where t is in s. If necessary, round your answers to three significant figures. Determine: Part A The amplitude. Express your answer with the appropriate units. Value Units Submit Request Answer Part B The period. Express your answer with the appropriate units. Units Submit Request Answer Part C The spring constant. Express your answer with the appropriate units.

Solution Steps

• The amplitude $A$ is the coefficient of the cosine function in the position equation.
• Given $x(t) = (2.0 \, \text{cm}) \cos(10t - \pi/4)$, the amplitude $A$ is $2.0 \, \text{cm}$.

• The angular frequency $\omega$ is given in the cosine function argument.
• Given $x(t) = (2.0 \, \text{cm}) \cos(10t - \pi/4)$, the angular frequency $\omega$ is $10 \, \text{rad/s}$.
• The period $T$ is related to the angular frequency by $T = \frac{2\pi}{\omega}$.
• Calculate $T$: $T = \frac{2\pi}{10} = 0.628 \, \text{s}$.

• Use the formula for the angular frequency $\omega = \sqrt{\frac{k}{m}}$.
• Rearrange to solve for the spring constant $k$: $k = m\omega^2$.
• Given mass $m = 50 \, \text{g} = 0.050 \, \text{kg}$ and $\omega = 10 \, \text{rad/s}$.
• Calculate $k$: $k = 0.050 \times (10)^2 = 5.00 \, \text{N/m}$.

Final Answer