Harmonic oscillator

Calculate the total energy of a body performing a harmonic oscillating motion if its mass is 200 g, the amplitude of the deflection is 2 cm and the frequency is 5 Hz. Round the result to 3 decimal places.

Correct result:

E =  0.0395 J

Solution:

$$\begin{gathered} m=200\text{ g}\to \text{ kg}=200\mathrm{/}1000\text{ kg}=0.2\text{ kg } \\ x=2\text{ cm}\to \text{ m}=2\mathrm{/}100\text{ m}=0.02\text{ m } \\ f=5\text{ Hz } \\ g=9.81{\text{m/s}}^2 \\ T=1\mathrm{/}f=1\mathrm{/}5={\displaystyle \frac{1}{5}}=0.2\text{ s } \\ \omega =2\pi \cdot f=2\cdot 3.1416\cdot 5\doteq 31.41591\text{/rad } \\ f={\displaystyle \frac{1}{2\pi }}\cdot \sqrt{{\displaystyle \frac{k}{m}}} \\ k={\omega }^2\cdot m=31.4159^2\cdot 0.2\doteq 197.3921 \\ E={\displaystyle \frac{1}{2}}\cdot k\cdot x^2={\displaystyle \frac{1}{2}}\cdot 197.3921\cdot 0.02^2=0.0395\text{ J} \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Wave parameters
  Calculate the speed of a wave if the frequency is 336 Hz and the wavelength is 10 m.
• Circle arc
  Calculate the area of the circular arc in m² where the diameter is 290 dm and a central angle is 135°. Result round to three decimal places.
• Circular motion
  Mass point moves moves uniformly in a circle with radius r = 3.4 m angular velocity ω = 3.6 rad/s. Calculate the period, frequency, and the centripetal acceleration of this movement.
• Rotaty motion
  What is the minimum speed and frequency that we need to rotate with water can in a vertical plane along a circle with a radius of 70 cm to prevent water from spilling?
• Inclined plane
  1. How much work W we have to do to pull a body weighing 200 kg along an inclined plane with a length of 4 m to a total height of 1.5 m. 2. Find the force we need to exert to do this if we neglect frictional resistance. 3. Find the force we would need if
• Cu wire
  Copper wire has a length l = 980 m and diameter d = 8 mm. Calculate the weight if density of copper is ρ = 8500 kg/m³. Result round to one decimal place.
• Concrete column
  The concrete column of the highway bridge has the shape of a block with dimensions of 1m x 0.8m x 25m. It should be lifted by crane to a height of 20m. What is the power of his engine if the lifting takes 2 minutes?
• Accelerated motion - mechanics
  The delivery truck with a total weight of 3.6 t accelerates from 76km/h to 130km/h in the 0.286 km long way. How much was the force needed to achieve this acceleration?
• Hairs
  Suppose the length of the hair is affected by only the α-keratin synthesis, which is the major component. This synthesis takes place in the epithelial cells of the hair bulb. The structure of α-keratin is made up of α-helix, wherein in one revolution it i
• The glass
  1 m³ of glass weighs 2600 kg. Calculate the weight of the glass glazing panel with dimensions of 2.5 m and 3.8 m if the thickness of the glass is 0.8 cm
• Decagon prism
  A regular decagon of side a = 2 cm is the base of the perpendicular prism, the side walls are squares. Find the prism volume in cm³, round to two decimal places.
• Constant Angular Acceleration
  The particle began to move from rest along a circle with a constant angular acceleration. After five cycles (n = 5), its angular velocity reached the value ω = 12 rad/s. Calculate the magnitude of the angular acceleration E of this motion and the time int
• Train
  The train is running at speeds of 96 km/h. From the beginning of braking to full stop train run for 3.3 minutes. If the train slows the braking equally, calculate the distance of the place from the station where you need to start to brake.
• Water level
  To cuoid shaped poll, bottom size 2m and 3.5m; flows water at a rate of 50 liters per minute. How long will take to water reach level 50 cm?
• Friction coefficient
  What is the weight of a car when it moves on a horizontal road at a speed of v = 50 km/h at engine power P = 7 kW? The friction coefficient is 0.07
• Shot
  Shot with a mass 43 g flying at 256 m/s penetrates into the wood to a depth 25 cm. What is the average force of resistance of wood?
• Self-oscillation period
  The water in the vessel carried by the boy has a self-oscillation period of 0.8 s. What is the size of the boy's movement speed when the length of the boy's step is 60 cm? Give the result in m/s.