The set of angles α satisfying sin α = 0 and COS = - 1 is

The set of angles α satisfying sin α = 0 and COS = - 1 is

The set of angles α satisfying sin α = 0 and COS = - 1 is {α | α = 2K π + π, K ∈ Z}

The vibration equation is x = ACOS (WT + 1 / 2 π), the ratio of kinetic energy at t = 0 to kinetic energy at t = t / 8
When a body vibrates harmonically, the equation is x = ACOS (WT + π / 2). What is the ratio of the kinetic energy at t = 0 to that at t = t / 8?

The derivative of T for x = ACOS (WT + π / 2) is obtained, and the velocity v = ω asin ω T, ω = 2 π / T is obtained
V1 = ω a when t = 0, V2 = ω A / √ 2 when t = t / 8
So kinetic energy EK1: Ek2 = 2:1

The vibration equation of a body in simple harmonic motion is x = ACOS (WT + 1 / 2 π), the potential energy ratio and kinetic energy ratio at t = 0 and T = t / 8

Because the total energy is: e = 1 / 2kA ^ 2
When t = 0, x = 0
Ep=0；Ek=1/2kA^2
When t = t / 8, x = - the root of two
Ep=1/4KA^2=1/2E,Ek=E-E/2=E/2
So the ratio of potential energy to kinetic energy at t = 0: 0
When t = t / 8, the ratio of potential energy to kinetic energy is 1:1

How to calculate the initial phase of simple harmonic motion?
Because trigonometric function has periodicity, can there be many initial phases?

You can work out the function according to the image, and the value of FAI (that is, the value in brackets when x equals zero) is the initial phase

What is the initial phase of simple harmonic motion

When t = 0, the initial phase of simple harmonic motion is the angle of the object in uniform circular motion away from the diameter (counterclockwise is the positive direction). When t = 0 on the image, the intersection point of the object and the y-axis, um, should have the same value. The phase is the physical quantity reflecting the state of the object at any time. In the trigonometric function, 2 π

What are the concepts of phase and initial phase of simple harmonic motion?
The book only says that ω x + ψ is the phase, and when x = 0, ψ is called the initial phase. So what is the phase? Is it useful?

When t = 0, the initial phase of simple harmonic motion is the angle of the object in uniform circular motion away from the diameter (counterclockwise is the positive direction). When t = 0 on the image, the intersection point of the object and the y-axis, um, should have the same value. The phase is the physical quantity reflecting the state of the object at any time. In the trigonometric function, 2 π

The phase and initial phase of harmonic motion y = 3sin (5x + π / 4) are________

The phase is 5x + π / 4 and the initial phase is π / 4

Definition of initial phase of simple harmonic motion
How to judge which simple harmonic motion with the same period leads by image

If the extension direction of the image is the positive direction of the X axis, the first image can form another image by moving a unit to the right, and a

∫1/cos^3(t)dt

∫1/cos^3(t)dt
= ∫sec^3(t)dt
= ∫sect dtant
= sect tant - ∫tant dsect
= sect tant - ∫tan^2 t sect dt
= sect tant - ∫(sec^2 t - 1) sect dt
= sect tant - ∫sec^3 t dt + ∫sect dt
= sect tant - ∫sec^3 t dt + ln|tant+sect|
therefore
2∫sec^3 t dt = sect tant + ln|tant+sect|
∫sec^3 t dt = (1/2) sect tant + (1/2) ln|tant+sect|

Solving ∫ t * cos (1 / T) DT

Just explain what ∫ means