Show me your work make it clear please A particle executes simple harmonic motio

Question

Show me your work make it clear please A particle executes simple harmonic motion with an amplitude of 3.00 cm. At what displacement from the midpoint of its motion does the speed equal 1/2 of its maximum speed? An automobile having a mass of 1000 kg is driven into a brick wall in a safety test. The bumper behaves like a spring of constant 5.0 Times 10^6 N/m and compresses 3.16 cm as the car is brought to re the speed of the car before impact assuming no energy was lost during impact with the wall? A block of unknown mass is attached to a spring of spring constant 6.5 N/m and undergoes simple harmonic motion with an amplitude of 10 cm. When the mass is halfway between its equilibrium p endpoint, its speed is measured to be 30 cm/s. Calculate the mass of the block. Find the period of the motion. Calculate the maximum acceleration of the block. You need to know the height of a tower, but darkness obscures the ceiling. You note that a pendulum extending from the ceiling almost touches the floor and that its period is 24 s. How tall is the tower? Having landed on a newly discovered planet, an astronaut sets up a simple pendulum of length 1.7 m and finds that it makes 150 complete oscillations in 592 s. The amplitude of the oscillations is very small compared to the pendulum's length. What is the gravitational acceleration on the surface of this planet? A certain pendulum clock that works perfectly on Earth is taken to the moon, where g = 1.63 m/s^2. The clock is started at 12:00:00 A M. and runs for 24 h. What will be the reading for the hours? What will be the reading for the minutes? What will be the reading for the seconds?

Explanation / Answer

3)

Given that

A particle executessimple harmonic motion with an amplitude (A) =3.00cm

We know that from the conservation of energy

Total energy =KE+PE =E+U

(1/2)kA2 =(1/2)mvmax2+(1/2)kx2

We also know that vmax =Aw

=Aw/2

From the above we get x2 =(3/4)A2

x =1.732A/2 =2.598cm

4)

The compression energy is given by

E =(1/2)kx2 =0.5*(5*106)(0.0316)2 =2.496kJ

This energy is due to the kientic energy =(1/2)mv2

Then v =Sqrt(2E/m) =Sqrt(2*2.496*103J/1000) =2.2342m/s

6)

We know that time period of the pendulum is given by

T =2piSqrt(L/g)

T2 =4pi2*L/g

Then L =g*T2/4pi2 =9.81*(24)2/4*(3.14)2=143.275m

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.