Question

The Terrible Tinkerer—an evil-doing engineer—has trapped a frightened citizen on a 700 kg horizontally oscillating platform. The effective spring constant of the oscillator is 200 N/m and the mass of the citizen, who understandably is clinging on to the platform for dear life, is 70.0 kg. It all started when the unsuspecting citizen stepped onto the platform while high upon a bridge. The trapped platform then broke away and began oscillating starting from rest +40.0 m from equilibrium carrying the unsuspecting citizen with it.

a) What is the angular frequency and frequency of the motion?

b) What is the period?

c) What are the amplitude and phase angle?

d) What is the total energy of the oscillator?

e) If it will take Spider-Man 9.20 seconds to arrive where will the platform & citizen be (location, x)?

f) What will be their velocity at 9.2 seconds in m/s and mph?

g) What is the maximum horizontal acceleration experienced by the citizen in g’s?

h) Spider-Man—being a good physicist—waits until the platform is at ? = +? again to carefully remove the citizen from the platform. How long after 9.20 seconds does he have to wait?

i) What is the period of oscillation after the citizen is removed?

j) What is the total energy of the oscillator after the citizen is removed?

Answer 1

Answer:-

Given that

The Terrible Tinker-an evil -doing engineer - has trapped a frightened citizen on a 700 kg

The effective spring constant of the oscillator is 200 N/m

mass of citizen, who is clinging on to the platform for dear life is 70.0 kg.

The trapped platform then broke away and began oscillating starting from rest + 40.0 m

Total mass of system = mass of platform + mass of citizen

= 700 kg + 70 kg

= 770 kg

Given k = 200 N/m

(a) Angular frequency,

= 0.51 rad/sec

frequency

(b)

Time period

(c)

Amplitude = maximum displacement from the equilibrium = 40 m

Equation of motion

at t = 0, x = A (maximum displaced from equilibrium)

so, phase angle = 90⁰

^(d)

^{Total energy,}

= 160000 J

^(e)

Equation of motion:

  

given, t = 9.2 s

A = + 40 m

w = 0.51 rad/sec

   = 90⁰

x = (40 m) cos(0.51 9.2) = -0.81 m

(f)

From conservation of energy

Here A = 40 m

x = -0.81 m

= 20.38 m/s

(g)

Force at maximum position,

F = k A = 200 N/m 40 m = 8000 N

Acceleration,

  

= 10.39 m/s²

(h)

spider man has to wait for (12.345 - 9.2)s

= 3.145 s

(i)

After citizen is removed, m = 700 kg

k = 200 N/m