This chapter explores the concept of oscillations, including periodic and oscillatory motions which are fundamental to understanding various physical phenomena.
Oscillations – Formula & Equation Sheet
Essential formulas and equations from Physics Part - II, tailored for Class 11 in Physics.
This one-pager compiles key formulas and equations from the Oscillations chapter of Physics Part - II. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
ν = 1/T
ν represents frequency (in hertz), T is the period (in seconds). This formula relates frequency and period, indicating how many cycles occur in one second.
T = 2π√(m/k)
T is the period (in seconds), m is mass (in kg), and k is the spring constant (in N/m). This formula gives the period of a mass-spring system in simple harmonic motion.
ω = 2πν
ω is the angular frequency (in radians/second), and ν is the frequency (in hertz). It provides a link between angular frequency and frequency.
x(t) = A cos(ωt + φ)
x(t) is the displacement (in meters) at time t, A is amplitude (maximum displacement), ω is angular frequency, and φ is the phase constant. This is the basic equation of simple harmonic motion.
v(t) = -Aω sin(ωt + φ)
v(t) is the velocity (in m/s) at time t, A is amplitude, and ω is angular frequency. This equation shows how the velocity varies over time in SHM.
a(t) = -Aω² cos(ωt + φ)
a(t) is the acceleration (in m/s²) at time t. The negative sign indicates that acceleration is directed towards the mean position.
E = 1/2 k A²
E is the total mechanical energy (in joules) of a simple harmonic oscillator, k is the spring constant, and A is the amplitude. This equation shows that total energy is constant in SHM.
U = 1/2 k x²
U is the potential energy (in joules), k is the spring constant, and x is the displacement (in meters). It represents the stored energy in the spring when displaced.
K = 1/2 m v²
K is the kinetic energy (in joules), m is mass (in kg), and v is velocity (in m/s). It quantifies the energy of an object in motion.
L = (gT²)/(4π²)
L is the length of a simple pendulum (in meters), g is the acceleration due to gravity (in m/s²), and T is the period of the pendulum (in seconds). This gives the relation between the length of a pendulum and its period.
Equations
F = -kx
F is the restoring force (in newtons), k is the spring constant (in N/m), and x is the displacement from equilibrium (in meters). It shows that force in SHM is proportional and opposite to the displacement.
T = 2π√(L/g)
T is the period (in seconds) of a simple pendulum, L is the length (in meters), and g is the acceleration due to gravity (in m/s²). This describes pendulum motion for small angles.
ω = 2π/T
ω is the angular frequency (in radians/second) and T is the period (in seconds). It relates the frequency of oscillation to the period.
x(t) = A cos(ωt + φ) or A sin(ωt + φ)
x(t) describes the displacement of a particle in SHM. Depending on conditions, it can be expressed using cosine or sine functions with amplitude A.
v(t) = dx/dt
This indicates that the velocity at any time t is the derivative of displacement with respect to time.
a(t) = dv/dt
This defines that the acceleration at any time t is the derivative of velocity with respect to time.
F(t) = ma(t)
This is Newton's second law where the force acting on an oscillating body is equal to the mass of the body multiplied by its acceleration.
E = K + U
This expresses the conservation of mechanical energy in the system where E is total energy, K is kinetic energy, and U is potential energy.
T = 2π√(m/k)
This gives the formula for the period of a mass on a spring, linking mass, spring constant and period.
x = A cos(ωt) + B sin(ωt)
A general solution for SHM, where A and B are constants that can be determined by initial conditions.
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