- PCB Study Material
- Online Test Series
- 5 Mock Tests
- 5 Diagnostic Tests
- 15 Practice Tests
- Sample Papers With Solutions
- Past Year Papers with Solutions
- Ask The Expert
- On Call Mentorship
Velocity is maximum at the mean position and minimum at the extremes.
Maximum velocity ; minimum velocity v = 0
Acceleration of a particle:
Acceleration is maximum at the extremes and minimum at the mean position.
Maximum acceleration ; minimum acceleration a = 0
Same phase SHM
Opposite phase SHM
Relation between phase difference and time difference
Energy of a body in SHM:
Total energy of a particle in SHM consists of two parts—kinetic energy (KE) and potential energy (PE). The sum of PE and KE remains constant.
At the mean position, kinetic energy is maximum and potential energy is minimum.
At the extreme position, kinetic energy is zero and potential energy is maximum.
Kinetic energy K
Potential energy U
Total energy = K + U
Superposition of two SHMs:
In the same direction and of the same frequency:
In the same direction but of different frequencies:
Resultant motion is not SHM.
In two perpendicular directions,
Case 1: If , the path will be a straight line and the amplitude will be
Case 2: If , the path will be an ellipse. The resultant motion is not SHM.
Spring mass system:
Time period of the spring mass system oscillating in the horizontal plane =
Time period of the spring mass system oscillating in the vertical plane =
Series combination of springs
Parallel combination of springs
Spring cut into two parts in the ratio m:n
Oscillation of a two-particle system:
Time period of the blocks
Amplitude of the blocks
Time period when the point of suspension is accelerating up=
Time period when the point of suspension is accelerating down =
Time period when the pendulum is accelerating horizontally =
Time period when the pendulum is accelerating down an inclined plane =
Oscillation of a floating body in a liquid:
= density of liquid
= density of solid
Motion of a ball in a tunnel through the earth:
Sound is a mechanical and longitudinal wave created by a vibrating source. It needs a medium for its propagation. In a longitudinal wave, particles of the medium vibrate in the direction of the propagation of the wave.
In a transverse wave, particles of the medium oscillate along the direction of the propagation of the wave?
Wavelength of a progressive wave is the distance between two consecutive points of the same phase at a given time. In a stationary wave, it is twice the distance between two consecutive nodes or antinodes.
Speed of sound wave:
Speed of a sound wave depends on elastic and inertial properties of the medium.
Speed of sound wave by Newton’s formula:
According to Newton, when sound propagates, the temperature of the gas remains constant. The velocity of sound in air is 280 m/s.
Laplace’s correction: According to Laplace, heat of the medium remains constant instead of its temperature; therefore, he replaced isothermal elasticity by adiabatic elasticity.
Factors affecting the speed of sound in a gas:
Effect of pressure: With a change in pressure, density also changes, and hence, pressure has no effect on the speed of sound in a gas.
Effect of temperature: , with rise in temperature, the velocity of sound in air increases by 0.61 m/s.
Effect of humidity: Speed of sound increases with increase in humidity.
Intensity of sound wave:
Intensity decreases in proportion to the square of the distance from the source.
When a source of sound and a listener are in motion relative to each other, the frequency of the sound heard by the listener is not the same as source frequency. The general formula for frequency is . Frequency tends to increase when the source and observer move close to each other and decreases when the source and observer move away from each other.
Principle of superposition of waves:
When two or more waves traverse the same medium, the displacement of any element of the medium is the algebraic sum of the displacement due to each wave.
Standing waves are the result of interference between longitudinal sound waves travelling in opposite directions. In a pipe open at both ends, the harmonics are given by , whereas for a pipe closed at one end, the harmonics are given by .
Interference of waves:
Constructive interference: The resultant amplitude is greater than the amplitude of individual waves.
Destructive interference: The resultant amplitude is less than the amplitude of individual waves.
Reflection of waves at fixed end and free end:
When a wave gets reflected from a fixed end, it suffers a phase change of π, i.e. it gets inverted.
When a wave gets reflected from a free end, the pulse is not inverted, but the free end overshoots twice the amplitude.
The general equation of the standing wave is given by . In standing waves, every element of the medium oscillates in SHM with the same angular frequency ω. The amplitude of SHM of a given element depends on the location x of the element in the medium.
Characteristics of stationary waves:
Disturbance does not move in any direction.
Minimum displacement points are called nodes, and maximum displacement points are called antinodes.
Amplitude of particles is different at different points.
Particles in a particular segment between two nodes vibrate in the same phase, but particles in neighbouring nodes vibrate in the opposite phase.
Resonance: When the frequency of the applied force is equal to one of the natural frequencies of the system, the amplitude of the resulting motion is the greatest.
Periodic variation in amplitude at a given point due to the superposition of two waves having slightly different frequencies.
A device used to measure the velocity of transverse mechanical waves.
Velocity of a wave in a string is given by
By learning in meritnation I got B2, but by learning topper learning I got A1... so which is the best. This is awesome to learn and easy to study science. At 1st term I got B2 but at 2nd term I got A1.
Manoj Vijay CBSE class IX
Excellent Faculty! I have been studying from topperlearning.com since Class IX and have consistently scored above 90% in my these 4 years.I studied throughout nights to achieve my goal.Moreover, becoming Rank 1 on topperlearning boosted my confidence to high skies.Thank you topperlearning, without you I would not have been able to score 91.2% in Class XII Boards(2015) and CGPA 9.8 in my Class X Boards(2013). Hope that topperlearning will continue to help students throughout India, creating a brighter future for them. Regards, Vivek Saahil
Vivek Saahil CBSE class XII Science
I like topper learning because I can understand the level I have prepared for my subject and study better.
Mohanapriya Saravanakumar CBSE class X
Topperlearning is really a very good helping tool. Every time I had doubts related to any concept in PCM I posted it and immediately my problem was solved. It also helped me in scoring good ranks in competitive exams too. The topper faculty is very good. The teachers explained each and every concept in depth. My favourite teacher is Physics teacher
Sahibdeep Singh Sodhi CBSE class XII Science
We all know that audio-visual medium is a better way of explaining and educating the students. It not only makes learning fun but also gives the message more clearly and precisely. Topper is a very good amalgamation of good teaching and good learning methods.
Sonia Malik, Professor
VV DAV School, New Delhi class ALL Class
Queries asked on Sunday and after 7 pm from Monday to Saturday will be answered after 12 pm the next working day.
Q.no 10 to 16 send me solutions sir.
Please give me solutions sir