Question

the displacement y of an oscillating particle varies with time t according equation y =2sin(0.5π+π/4) where why is in meter and t is in second find. (1) the amplitude. (2) the time period . (3) maximum velocity .(4) maximum accleration of particle ​

Answer 1

Solution :

As per the given data ,

• y = 2 sin (0.5π+π/4)

The equation of transverse wave travelling in the negative - y direction

• y = A sin (ωt + kx )

here ,

• A = amplitude
• ω = angular velocity
• k = wave number
• x = displacement

On comparing both the equations we get ,

→ A = 2

→ ω = 0.5π

→ k = π /4

→ x = 1

(1) Amplitude

⇒ A = 2 m

(2) Time period

⇒ T = 2π / ω

⇒ T = 2x π x 2 / π

⇒ T = 4 s

(3) Maximum velocity

⇒ v = Aω

⇒ v = 2 x π / 2

⇒ v = π

⇒ v = 3.14 m/s

(4) Maximum acceleration

⇒ a = Aω²

⇒ a = 2 x π² / 4

⇒ a = π² / 2

⇒ a = 3.14 x 3.14 / 2

⇒ a ≈ 9.8 / 2

⇒ a ≈ 4.9 m /s²

Answer 2

Answer:

4.9m/s² is the answer for the above questions