A spring 1.50 m long with force constant 460 N/m is hung from the ceiling of an elevator, and a block of mass 14.0 kg is attached to the bottom of the spring. (a) By how much is the spring stretched when the block is slowly lowered to its equilibrium point? (Enter the magnitude only.) m (b) If the elevator subsequently accelerates upward at 1.68 m/s', what is the position of the block, taking the equilibrium position found in part (a) as y = 0 and upwards as the positive y-direction. (Indicate the direction with the sign of your answer.) m (c) If the elevator cable snaps during the acceleration, describe the subsequent motion of the block relative to the freely falling elevator. What is the amplitude of its motion? m
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
![**Spring and Mass System in an Elevator**
A spring 1.50 m long with a force constant of 460 N/m is hung from the ceiling of an elevator, and a block of mass 14.0 kg is attached to the bottom of the spring.
**Questions:**
**(a)** By how much is the spring stretched when the block is slowly lowered to its equilibrium point? (Enter the magnitude only.)
\[ \_\_\_\_ \text{ m} \]
**(b)** If the elevator subsequently accelerates upward at 1.68 m/s², what is the position of the block, taking the equilibrium position found in part (a) as \( y = 0 \) and upwards as the positive y-direction? (Indicate the direction with the sign of your answer.)
\[ \_\_\_\_ \text{ m} \]
**(c)** If the elevator cable snaps during the acceleration, describe the subsequent motion of the block relative to the freely falling elevator. What is the amplitude of its motion?
\[ \_\_\_\_ \text{ m} \]
**Additional Materials:**
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This exercise explores the dynamics of a spring-mass system within an accelerating elevator, addressing concepts of equilibrium, forces, and motion.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F590afbf9-816f-4ea8-ba94-a1e0761dc0e5%2Fb262b54f-13ba-4ad7-8166-4daa5ef8b9da%2F58l78w_processed.png&w=3840&q=75)
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