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