Please answer this question clearly with all steps. Thank you so much!(3) **Problem Statement:**A mass \( m = 0.4 \, \text{kg} \) is attached to a vertical hanging spring, which obeys Hooke's Law. After hanging the weight, the spring is stretched from its equilibrium position by \( \Delta y_0 = 0.1 \, \text{m} \). The mass is then extended an additional \( \Delta y = 0.1 \, \text{m} \) upward and released from rest. The period of this system is**Options:**(a) \( T = 0.010 \, \text{s} \) (b) \( T = 0.063 \, \text{s} \) (c) \( T = 0.100 \, \text{s} \) (d) \( T = 0.628 \, \text{s} \) ---**Explanation:**The problem involves a vertical spring-mass system. The goal is to determine the period \( T \) of the oscillation of the mass attached to the spring. The period is the time it takes to complete one full oscillation. The system obeys Hooke's Law, which describes the force exerted by a spring as proportional to its displacement from the equilibrium position. The period of a mass-spring system can be calculated using the formula:\[ T = 2\pi \sqrt{\frac{m}{k}} \]where \( m \) is the mass and \( k \) is the spring constant. Here, \( m = 0.4 \, \text{kg} \). The problem requires understanding the relationship between the stretch of the spring and the properties of the oscillation to find the correct period from the given options.

Name: Please answer this question clearly with all steps. Thank you so much!
Uploaded: 2024-03-20T06:58:04.000Z
Channel: Bartleby
Description: Please answer this question clearly with all steps. Thank you so much!(3) **Problem Statement:**A mass \( m = 0.4 \, \text{kg} \) is attached to a vertical hanging spring, which obeys Hooke's Law. After hanging the weight, the spring is stretched fro