PHYSICS TUTOR IN MUMBAI NEET

Physics Tutor in Napean Sea Road Mumbai

NEET • IIT JEE • CBSE • IB • IGCSE • Edexcel • A-Level • AP Physics

Kumar Sir Physics Classes

☎ +91-9958461445

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✉ kumarsirphysics@gmail.com

y = A sin ωt

v = Aω cos ωt

a = −ω²y

T = 2π/ω

ω = 2π/T

Spring: T = 2π√(m/k)

Pendulum: T = 2π√(l/g)

U-Tube: T = 2π√(L/2g)

Energy: E = ½kA²

vmax = Aω

amax = Aω²

Earth Tunnel: T = 2π√(R/g)

Physics Tutor in Napean Sea Road Mumbai

+91-9958461445

If you live in Napean Sea Road Mumbai and you are preparing for NEET, IIT JEE, CBSE, IB, IGCSE, Edexcel, A-Level or AP Physics, then chapters like Simple Harmonic Motion can become very confusing if your fundamentals are weak.

Let us take this question:

For the spring pendulum shown in the figure, spring constant is 3 × 10⁴ N/m, amplitude of oscillation is 0.1 m and total mechanical energy is 200 J. Which statement is not true?

For a spring oscillator:

Maximum kinetic energy = Total energy − Minimum potential energy

Spring potential energy at amplitude:

PE = 1/2 kA²

Now,

PE = 1/2 × 3 × 10⁴ × (0.1)²

PE = 1/2 × 30000 × 0.01

PE = 150 J

So, spring energy due to oscillation is 150 J.

But total mechanical energy is given as 200 J. That means there may be an extra constant potential energy of 50 J in the system.

So:

Minimum PE = 50 J
Maximum PE = 200 J
Maximum KE = 150 J

This type of question is not only about formula. It checks whether the student understands energy variation in SHM.

If you are unable to solve such questions, it means your SHM concept needs improvement. If SHM is weak, then Waves will also become weak. If Waves is weak, then Wave Optics will also become difficult. That is why Physics should not be studied by memorising formulas only.

Kumar Sir explains these questions step by step. First, he explains what total mechanical energy means. Then he explains potential energy, kinetic energy, amplitude, mean position and extreme position. After that, he connects the formula with the actual question.

If you live in Napean Sea Road Mumbai, you can contact Kumar Sir for online Physics classes. You can take an interaction or demo discussion and understand how Physics can become clear with the right guidance.

Call / WhatsApp: +91-9958461445
Email: kumarsirphysics@gmail.com
Website: Kumar Physics Classes

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Final Message

If you are living in Napean Sea Road Mumbai and Physics is becoming stressful, do not ignore the problem. SHM, Waves, Wave Optics, Mechanics and Electricity all require strong fundamentals. Kumar Sir can help you build those fundamentals with proper explanation, notes, numerical practice and doubt clearing.

Contact Kumar Sir: +91-9958461445
Email: kumarsirphysics@gmail.com
Website: kumarphysicsclasses.com

Oscillations and Simple Harmonic Motion

Oscillation means repeated to-and-fro motion about a mean position. In Physics, oscillations are very important because they connect mechanics, waves, sound, wave optics and many advanced topics. A student who understands oscillation properly can easily understand Simple Harmonic Motion, spring motion, simple pendulum, U-tube liquid oscillation, damped oscillation and forced oscillation.

Basic SHM Equations

For a particle performing Simple Harmonic Motion, displacement can be written as:

y = A sin ωt

Here, A is amplitude, ω is angular frequency and t is time.

Velocity is obtained by differentiating displacement with respect to time:

v = Aω cos ωt

Acceleration is obtained by differentiating velocity:

a = -Aω² sin ωt

Since y = A sin ωt, acceleration can also be written as:

a = -ω²y

This negative sign is the heart of SHM. It shows that acceleration is always directed opposite to displacement and towards the mean position.

Oscillatory Motion, Periodic Motion and Non-Periodic Motion

Oscillatory Motion: Motion repeated about a fixed mean position is called oscillatory motion. Example: simple pendulum.
Periodic Motion: Motion repeated after equal intervals of time is called periodic motion. Example: uniform circular motion.
Non-Periodic Motion: Motion which does not repeat after equal intervals of time is called non-periodic motion. Example: motion of a vehicle in traffic.
Important: Every SHM is periodic, but every periodic motion is not SHM.

Simple Pendulum

A simple pendulum consists of a small heavy bob suspended by a light inextensible string. For small angular displacement, restoring force acts towards the mean position and the pendulum performs SHM.

T = 2π√(l / g)

Here, l is length of pendulum and g is acceleration due to gravity.

Liquid Oscillation in U-Tube

When liquid in a U-tube is slightly displaced and released, it performs SHM. The restoring force is due to the difference in height of liquid columns.

T = 2π√(l / 2g)

Here, l is the total length of liquid column in the U-tube. This result is very important for NEET and IIT JEE.

Spring-Mass Oscillation

When a mass is attached to a spring and displaced from equilibrium, spring force acts as restoring force.

F = -kx

For SHM:

F = -mω²x

Comparing both:

ω = √(k / m)

T = 2π√(m / k)

Here, k is spring constant and m is mass attached to the spring.

Effect of Temperature on Simple Pendulum

When temperature increases, the length of the pendulum increases due to linear expansion. Since time period depends on square root of length, time period also increases.

T = 2π√(l / g)

If temperature increases by Δθ and coefficient of linear expansion is α, then:

T' = T(1 + αΔθ / 2)

So, a pendulum clock becomes slow in summer because its time period increases.

Damped Oscillation

Damped oscillation is the oscillation in which amplitude decreases with time due to resistive forces like air resistance, friction or viscosity.

Amplitude decreases with time

Example: a pendulum slowly stops after some time because energy is lost to the surroundings.

Undamped Oscillation

Undamped oscillation is an ideal oscillation in which there is no energy loss and amplitude remains constant forever.

Amplitude remains constant

In real life, perfectly undamped oscillation is not possible, but it is used as an ideal model in Physics.

Final Summary

Displacement in SHM: y = A sin ωt
Velocity in SHM: v = Aω cos ωt
Acceleration in SHM: a = -Aω² sin ωt
SHM condition: a = -ω²y
Simple pendulum: T = 2π√(l/g)
U-tube liquid oscillation: T = 2π√(l/2g)
Spring-mass system: T = 2π√(m/k)
Temperature rise increases pendulum time period.
Damped oscillation has decreasing amplitude.
Undamped oscillation has constant amplitude.

SHM of an Object Dropped Through a Tunnel Inside Earth

Suppose a straight tunnel is made through the Earth and an object is released inside it. If we ignore air resistance and assume Earth has uniform density, then the object will perform Simple Harmonic Motion about the centre of Earth.

Object oscillates through the tunnel about Earth’s centre

Derivation of Time Period

Let the object be at a distance x from the centre of Earth. Inside Earth, gravitational acceleration is not constant. It decreases linearly with distance from the centre.

g' = g x / R

Here, R is radius of Earth and g is acceleration due to gravity on the surface of Earth.

Force on the object at distance x from the centre:

F = -m g'

F = -m(gx/R)

F = -(mg/R)x

This force is directly proportional to displacement x and directed towards the centre. Therefore, this is a restoring force and the motion is SHM.

Compare with SHM Equation

F = -mω²x

Now compare:

mω²x = mgx/R

ω² = g/R

ω = √(g/R)

Time Period

T = 2π/ω

T = 2π√(R/g)

This is the final expression for the time period of an object oscillating through a tunnel inside Earth.

Final Result

T = 2π√(R/g)

For Earth, this time period is approximately:

T ≈ 84.6 minutes

So, if an object is dropped into a frictionless tunnel through Earth, it will reach the other side and come back again, performing SHM continuously. This result is very important for NEET Physics, IIT JEE Physics, CBSE Class 11 Physics, A-Level Physics and AP Physics.