Question

Груз массой 1 кг , прикреплённый к пружине жёсткостью 400 Н/м, удерживается в положении, когда пружина не деформирована. Какую максимальную скорость будет иметь груз, если его отпустить без толчка и позволить совершать вертикальные гармонические колебания?

Answer 1

Правильно или нет, судите...
На пружинку действует 2 силы mg=kx (причём, когда отпустят x=A)
x=10/400=0,025м
u=wA
u=2pA/T=2pA/2p sqrt (m/k) = A sqrt (K) / sqrt (m) = 0,025 *20 = 0,5 м/c

Answer 2

Vertical Harmonic Oscillation of a 1 kg Mass Attached to a Spring

When a 1 kg mass is attached to a spring with a stiffness of 400 N/m and is held in a position where the spring is not deformed, the maximum speed the mass will have when released without a push and allowed to perform vertical harmonic oscillations can be calculated.

To find the maximum speed of the mass, we can use the formula for the maximum speed in vertical harmonic motion, which is given by:

v = Aω

Where: - v is the maximum speed - A is the amplitude of the oscillation - ω is the angular frequency

The amplitude of the oscillation can be determined from the initial conditions, and the angular frequency can be calculated using the formula:

ω = √(k/m)

Where: - k is the spring constant (stiffness) - m is the mass

Let's calculate the maximum speed using the given values.

Using the given stiffness of the spring (k = 400 N/m) and the mass (m = 1 kg), we can calculate the angular frequency (ω) and then determine the maximum speed (v).

Calculation

First, let's calculate the angular frequency (ω): ω = √(k/m) ω = √(400/1) ω = 20 rad/s [[2 #]]

Now, we can calculate the maximum speed (v): v = Aω

The amplitude (A) of the oscillation is not provided in the given information, so we'll calculate the maximum speed in terms of the angular frequency (ω).

v = Aω = A * 20

The maximum speed of the mass when released without a push and allowed to perform vertical harmonic oscillations will be directly proportional to the amplitude of the oscillation.

Therefore, the maximum speed of the mass can be determined once the amplitude of the oscillation is known.

If you have the specific amplitude of the oscillation, we can calculate the maximum speed using the formula v = Aω.