The restoring force F in Simple Harmonic Motion (SHM) obeys Hooke's Law, which is represented by the expression: F = -kx Here, the meanings of the parameters are as follows: - k is the force constant (spring constant), - x is the displacement from the equilibrium position. The negative sign shows thRead more
The restoring force F in Simple Harmonic Motion (SHM) obeys Hooke’s Law, which is represented by the expression:
F = -kx
Here, the meanings of the parameters are as follows:
– k is the force constant (spring constant),
– x is the displacement from the equilibrium position.
The negative sign shows that it always acts against the displacement in an attempt to bring the particle back to its equilibrium position.
The total energy (E) in Simple Harmonic Motion (SHM) is expressed as: E = (1/2) k A² where: - k is the force constant, - A is the amplitude. Because energy is proportional to A², if the amplitude A is doubled (2A), the total energy becomes: E' = (1/2) k (2A)² = 4 × (1/2) k A² = 4E So, the total enerRead more
The total energy (E) in Simple Harmonic Motion (SHM) is expressed as:
E = (1/2) k A²
where:
– k is the force constant,
– A is the amplitude.
Because energy is proportional to A², if the amplitude A is doubled (2A), the total energy becomes:
E’ = (1/2) k (2A)² = 4 × (1/2) k A² = 4E
So, the total energy becomes four times its initial value.
In Simple Harmonic Motion (SHM), the displacement x and velocity v are related as: x = A sin(ωt) v = dx/dt = Aω cos(ωt) Because sin(ωt) and cos(ωt) differ by a phase of π/2 rad, the phase difference between displacement and velocity is π/2 rad. Click here for more: https://www.tiwariacademy.com/ncerRead more
In Simple Harmonic Motion (SHM), the displacement x and velocity v are related as:
x = A sin(ωt)
v = dx/dt = Aω cos(ωt)
Because sin(ωt) and cos(ωt) differ by a phase of π/2 rad, the phase difference between displacement and velocity is π/2 rad.
For Simple Harmonic Motion (SHM), the velocity v is expressed by: v = Aω cos(ωt) The maximum velocity (v_max) is found when cos(ωt) = 1, hence: v_max = Aω where: - A is the amplitude, - ω is the angular frequency. Therefore, the maximum velocity of a simple harmonic oscillator is Aω. Click here forRead more
For Simple Harmonic Motion (SHM), the velocity v is expressed by:
v = Aω cos(ωt)
The maximum velocity (v_max) is found when cos(ωt) = 1, hence:
v_max = Aω
where:
– A is the amplitude,
– ω is the angular frequency.
Therefore, the maximum velocity of a simple harmonic oscillator is Aω.
In the wave equation y = A sin(kx – ωt): - k is the wave number, which describes the spatial frequency of the wave. In technical terms, it is defined as k = 2π/λ, where λ is the wavelength. - It tells how many wave cycles are accommodated in a unit distance. Therefore, k decides the waves' propagatiRead more
In the wave equation y = A sin(kx – ωt):
– k is the wave number, which describes the spatial frequency of the wave. In technical terms, it is defined as k = 2π/λ, where λ is the wavelength.
– It tells how many wave cycles are accommodated in a unit distance.
Therefore, k decides the waves’ propagation in space.
The restoring force in SHM is given by
The restoring force F in Simple Harmonic Motion (SHM) obeys Hooke's Law, which is represented by the expression: F = -kx Here, the meanings of the parameters are as follows: - k is the force constant (spring constant), - x is the displacement from the equilibrium position. The negative sign shows thRead more
The restoring force F in Simple Harmonic Motion (SHM) obeys Hooke’s Law, which is represented by the expression:
F = -kx
Here, the meanings of the parameters are as follows:
– k is the force constant (spring constant),
– x is the displacement from the equilibrium position.
The negative sign shows that it always acts against the displacement in an attempt to bring the particle back to its equilibrium position.
Click here for more:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-13/
If the amplitude of a simple harmonic motion is doubled, the total energy becomes
The total energy (E) in Simple Harmonic Motion (SHM) is expressed as: E = (1/2) k A² where: - k is the force constant, - A is the amplitude. Because energy is proportional to A², if the amplitude A is doubled (2A), the total energy becomes: E' = (1/2) k (2A)² = 4 × (1/2) k A² = 4E So, the total enerRead more
The total energy (E) in Simple Harmonic Motion (SHM) is expressed as:
E = (1/2) k A²
where:
– k is the force constant,
– A is the amplitude.
Because energy is proportional to A², if the amplitude A is doubled (2A), the total energy becomes:
E’ = (1/2) k (2A)² = 4 × (1/2) k A² = 4E
So, the total energy becomes four times its initial value.
Click here for more:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-13/
The phase difference between displacement and velocity in SHM is
In Simple Harmonic Motion (SHM), the displacement x and velocity v are related as: x = A sin(ωt) v = dx/dt = Aω cos(ωt) Because sin(ωt) and cos(ωt) differ by a phase of π/2 rad, the phase difference between displacement and velocity is π/2 rad. Click here for more: https://www.tiwariacademy.com/ncerRead more
In Simple Harmonic Motion (SHM), the displacement x and velocity v are related as:
x = A sin(ωt)
v = dx/dt = Aω cos(ωt)
Because sin(ωt) and cos(ωt) differ by a phase of π/2 rad, the phase difference between displacement and velocity is π/2 rad.
Click here for more:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-13/
The maximum velocity of a simple harmonic oscillator is
For Simple Harmonic Motion (SHM), the velocity v is expressed by: v = Aω cos(ωt) The maximum velocity (v_max) is found when cos(ωt) = 1, hence: v_max = Aω where: - A is the amplitude, - ω is the angular frequency. Therefore, the maximum velocity of a simple harmonic oscillator is Aω. Click here forRead more
For Simple Harmonic Motion (SHM), the velocity v is expressed by:
v = Aω cos(ωt)
The maximum velocity (v_max) is found when cos(ωt) = 1, hence:
v_max = Aω
where:
– A is the amplitude,
– ω is the angular frequency.
Therefore, the maximum velocity of a simple harmonic oscillator is Aω.
Click here for more:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-13/
The equation of a traveling wave is y = A sin(kx – ωt). The term k represents
In the wave equation y = A sin(kx – ωt): - k is the wave number, which describes the spatial frequency of the wave. In technical terms, it is defined as k = 2π/λ, where λ is the wavelength. - It tells how many wave cycles are accommodated in a unit distance. Therefore, k decides the waves' propagatiRead more
In the wave equation y = A sin(kx – ωt):
– k is the wave number, which describes the spatial frequency of the wave. In technical terms, it is defined as k = 2π/λ, where λ is the wavelength.
– It tells how many wave cycles are accommodated in a unit distance.
Therefore, k decides the waves’ propagation in space.
Click here for more:
See lesshttps://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-13/