A 100 .-g block hangs from a spring with k=5.00 N / m. At t=0 s, the block is 20.0 cm below t

step 1 In this problem given that mass of the block is equal to 100 gram which is equal to 0 .100 kg Al

A 100 .-g block hangs from a spring with k=5.00 N / m. At...

A 100 .-g block hangs from a spring with $k=5.00 \mathrm{~N} / \mathrm{m}$. At $t=0 \mathrm{~s}$, the block is $20.0 \mathrm{~cm}$ below the equilibrium position and moving upward with a speed of $200 . \mathrm{cm} / \mathrm{s}$. What is the block's speed when the displacement from equilibrium is $30.0 \mathrm{~cm} ?$

Key Concepts

Kinetic Energy

Kinetic energy represents the energy a body possesses due to its motion, expressed mathematically as 1/2 m v². In the context of oscillatory motion, as potential energy is converted to kinetic energy and vice versa, the value of the kinetic energy can be determined at various points along the motion, providing insight into the speed and dynamics of the oscillator.

Conservation of Mechanical Energy

The principle of conservation of mechanical energy asserts that in an isolated system with no non-conservative forces (like friction), the sum of kinetic and potential energy remains constant. In a mass-spring system, this means that the energy shifts between kinetic energy (energy of motion, 1/2 m v²) and potential energy (energy stored in the spring, 1/2 k x²), allowing for the prediction of the system's speed at various displacements.

Simple Harmonic Motion

Simple harmonic motion is the periodic oscillatory movement of a system where the acceleration is directly proportional to (and opposite in direction to) its displacement from an equilibrium position. This concept underpins the behavior of mass?spring systems, indicating that the system will oscillate symmetrically around its equilibrium point with a predictable frequency and amplitude.

Hooke's Law and Spring Potential Energy

Hooke's Law states that the force exerted by a spring is proportional to its displacement from equilibrium (F = -kx), where k is the spring constant. This law is vital in understanding how energy is stored in a spring; the potential energy stored is given by the formula U = 1/2 k x², which quantifies the elastic energy available as the system oscillates.

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