Spring-Mass SHM
Visualize simple harmonic motion with a spring-mass system. Watch energy transform between kinetic and potential forms.
Key Notes
The Work-Energy Theorem states: Net work done on a body equals the change in its kinetic energy (W_net = ΔKE).
Work done by a constant force: W = F·d·cos θ, where θ is the angle between force and displacement.
Conservative forces (gravity, spring) have associated potential energy. Non-conservative forces (friction) dissipate energy as heat.
For a spring: PE = ½kx², where k is the spring constant and x is the displacement from equilibrium.
In SHM (spring-mass system), energy continuously converts between KE and PE. Total mechanical energy is conserved.
Power is the rate of doing work: P = dW/dt = F·v (instantaneous power).
The area under a Force-displacement graph gives the work done.
At equilibrium position in SHM: KE is maximum and PE is minimum. At extreme positions: KE = 0, PE = maximum.
Formulas
Work Done
Work by a constant force at angle θ to displacement.
Work-Energy Theorem
Net work equals change in kinetic energy.
Spring PE
Potential energy stored in a spring displaced by x.
SHM Period (Spring)
Time period of oscillation for spring-mass system.
SHM Velocity
Velocity at displacement x, where A is amplitude.
Power
Instantaneous power.
Important Points
Work done by gravity is path-independent (conservative). Work by friction is path-dependent (non-conservative).
For a spring-mass SHM: ω = √(k/m), frequency f = ω/2π.
Total energy in SHM = ½kA² = constant (A is amplitude).
At x = A/√2, KE = PE (energy is equally divided).
Negative work by friction reduces mechanical energy. This 'lost' energy becomes heat.
In JEE, energy methods are often faster than force methods for solving kinematics problems.
Spring-Mass SHM notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.