A 30 g particle is undergoing simple harmonic motion with an amplitude of 2.0 ✕ 10-3 m and a maximum acceleration of magnitude 8.0 ✕ 103 m/s2. The phase constant is -π/2 rad. (a) Write an equation for the force on the particle as a function of time. (Use the following as necessary: t.) F = N (b) What is the period of the motion? s (c) What is the maximum speed of the particle? m/s (d) What is the total mechanical energy of this simple harmonic oscillator? J

Explanation:

Given:

Mass, m = 30 g

= 0.03 kg

Amplitude, A = 2.0 ✕ 10^-3 m

Maximum acceleration, am = 8.0 ✕ 10^3 m/s2

Phase constant, phil = -π/2 rad

Displacement, x = A cos(wt + phil)

dx/dt = v = -Aw sin(wt + phil)

dv/dt = a = -Aw^2 cos(wt + phil)

Force, f = mass × acceleration

F = -0.03 × Aw^2 cos(wt + phil)

B.

At am,

a = Aw^2

8.0 ✕ 10^3 = 2.0 ✕ 10^-3 × w^2

w = sqrt(4 × 10^6)

= 2 × 10^3 rad/s

But w = 2pi/T

Where T = period

T = 2pi/2000

= 3.142 × 10^-3 s

= 0.00314 s

C.

Velocity = Aw

= 2.0 ✕ 10^-3 × 2000

= 4 m/s

D.

Total mechanical energy = kinetic energy + potential energy

= 1/2mv^2 + mgx

= 0.03 × [1/2 × 4^2 + (9.8 × (2 × 10^-3 × cos(2π - π/2)))]

= 0.03 × (8 + 0)

= 0.24 J

i'm just gonna leave this comment here, so i can get a challange done-

explanation:

sleep paralysis is a parasomnia, events associated with sleep.

sleep paralysis happens when you are in the middle of waking up or falling asleep. it is the feeling of being conscious but unable to move. it definitely involves hallucinations.

i had a friend that had sleep paralysis and he told me a story one time where he was laying in bed and he couldn't move his body no matter how hard he tried and there was someone standing in the corner of his room coming towards him. he couldn't move and you can't "wake up" because you are already conscious. sometimes sleep paralysis can be triggered by frequent waking up during the night based off of multiple trips to the bathroom, or if you had ever been abused, sleep paralysis can start happening from things like that.