A mass of 125gm in suspended from a light spring, it vibrates with frequency of 2.6Hz. If the mass is reduced to 50gm and is suspended from the same spring. Find its frequency.
Question
A mass of 125gm in suspended from a light spring, it vibrates with frequency of 2.6Hz. If the mass is reduced to 50gm and is suspended from the same spring. Find its frequency.
Solution
Sure, let's solve this step by step.
Step 1: Understand the problem The problem is about simple harmonic motion. The frequency of vibration of a mass-spring system is given by the formula f = 1/2π √(k/m), where k is the spring constant and m is the mass.
Step 2: Find the spring constant First, we need to find the spring constant (k) using the given mass (125gm = 0.125kg) and frequency (2.6Hz). We can rearrange the formula to solve for k: k = m*(2πf)^2. Substituting the given values, we get k = 0.125*(2π*2.6)^2 = 21.205 kg/s^2.
Step 3: Find the new frequency Now, we can find the new frequency (f') using the new mass (50gm = 0.05kg) and the same spring constant. Rearranging the formula to solve for f', we get f' = 1/2π √(k/m') = 1/2π √(21.205/0.05) = 4.12 Hz.
So, if the mass is reduced to 50gm and is suspended from the same spring, its frequency will be approximately 4.12Hz.
Similar Questions
The period of motion of an object-spring system is T = 0.582 s when an object of mass m = 254 g is attached to the spring.(a) Find the frequency of motion in hertz. Hz(b) Find the force constant of the spring. N/m(c) If the total energy of the oscillating motion is 0.267 J, find the amplitude of the oscillations. m
The lowest resonant frequency for a spring is 0.750 flz. If the length of the spring is 5.60 m, what is thespeed of the wave in the spring?a. 4.20 m/s c. 6.00 m/sb. 5.60 m/s d. 8.40 m/s
A rod of length l,𝑙, mass m are connected to two springs of spring constant K𝐾 each. Find the frequency of small oscillation
A 1.13-kg mass attached to a spring is displaced 7.87 cm from the equilibrium position. It is released and then oscillates with a frequency of 4.05 Hz. What is the speed of the mass when it is 2.63 cm from the equilibrium position?
A mass of 1 kg is suspended from a spring of spring constant 25 Nm–1. If the undamped (or natural) frequency is times the damped frequency, calculate the damping constant in kg s–1.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.