Answer and Explanation:
Let:

The equation representing a simple harmonic motion, where:

As you may know the derivative of the position is the velocity and the derivative of the velocity is the acceleration. So we can get the velocity and the acceleration by deriving the position:

Also, you may know these fundamental formulas:

Now, using the previous information and the data provided by the problem, let's solve the questions:
(a)

(b)

(c)

(d)
We can extract the phase of the motion, the angular frequency and the amplitude from the equation provided by the problem:

(e)

(f)

Answer:
6.13 s
219 N
Explanation:
Newton's law in the x direction:
∑F = ma
150 cos 30° N − 50 N = (30 kg) a
a = 2.66 m/s²
Δx = v₀ t + ½ at²
(50 m) = (0 m/s) t + ½ (2.66 m/s²) t²
t = 6.13 s
Newton's law in the y direction:
∑F = ma
Fn + 150 sin 30° N − (30 kg) (9.8 m/s²) = 0
Fn = 219 N
Answer:
Explanation:
a) ωp = 2π radians / 1.7 s = <u>3.7 rad/s</u>
b) ωs = 3.7 rad/s(9.5 cm / 4.5 cm) = 7.8 rad/s
v = (ωs)R = 7.8(65) = 507 cm/s or <u>5.1 m/s</u>
c) ωs = 3.5 m/s / 0.65 m = 5.38 rad/s
ωp = 5.38(4.5 cm / 9.5 cm) = 2.55 rad/s
t = θ/ω = 2π / 2.55 = 2.463... <u>2.5 s</u>
Answer:

Explanation:
Given:
Solute Diffusion rate = 4.0 × 10⁻¹¹ kg/s
Area of cross-section = 0.50 cm²
Length of channel =0.25 cm
Now for the new channel
Area of cross-section = 0.30 cm²
Length of channel =0.10 cm
let the Solute Diffusion rate of new channel = s
now equating the diffusion rate per unit volume for both the channels

thus,
