Department of Mechanical Engineering, National Taiwan University
112-1 ME 1010 Introduction to Mechanical Engineering
Build and underst a MCK system
楊馥菱
TA: 黃澤樺, 蔡旻霖, 賴昱堯
1 Objective
Via team work, we build a simple MCK system to observe and measure the displacement of a mass
(M) under forces from the springs (K) and a damper (C). We also implement a transducer
(Ultrasonic Ranging Module) with its data I/O interface (UNO/Arduino) to achieve measurement.
2 Introduction
Simple harmonic motion (SHM) is a special type of periodic motion an object experiences due to a
restoring force whose magnitude is directly proportional to the distance of the object from an
equilibrium position and acts towards the equilibrium position. In an ideal MK system, the mass
oscillates periodically forever [1] but there are dissipative force (air drag, joint friction) that
eventually damps out the kinetic energy of an oscillating mass. To describe (predict) the dynamics
of the mass, the restoring force and the dissipative force are often approximated by a linear
mechanical model. Hence, we will build a tunable MCK system so that we can observe the dynamics
and compare it with the model’s prediction.
3 Tasks
Each team should
(1) find a way to achieve tunable M,
(2) calibrate the spring constants K via Hook’s law,
(3) develop a M-K (mass-spring) system and masure the mass displacement dynamics,
(4) build a dissipating environment with tunable damping strength C,
(5) develop a test facility to measure the mass dynamics to evaluate C.
4 Experiment set-up
4.1
List of equipment
We provide

Spring: stiff / soft springs (2)

Dashpot: 50 mL syringe (1), transparency (1), L-shape angle bracket* (4), fasteners (M4) (nut,
bolt washer) (4), PP sheet (1), storage box (1)

Arduino package: one set per person

Electric scale: classroom (Tue 12:10-13:10); TA office (reserve in advance via email)
112-1 機械工程概論 Project A
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Department of Mechanical Engineering, National Taiwan University
112-1 ME 1010 Introduction to Mechanical Engineering
Prepare on your own (try to use daily objects):

Mass: at least four values

Fixtures: for the MCK system, for the sensor/acturator
4.2
Demo test facility
Fig.1(a) shows a container holding heavy objects (M, coins, marble balls, water, softdrinks,…)
attached to two parallel springs (K) fixed to a framestructure. Fig.1(b) shows that a syringe is fixed
to the base of the container and this syringe will be immersed into water in Fig.1(c) so that drag
applied on the syringe creates damping (C) to the oscillation system. You may change the liquid
type to modify the damping strength but we may also add a close boundary to the syringe to affect
the liquid motion and to amplify the drag. Usually, thinner the gap, the greater the liquid drag and
so does the C value. To measure the mass oscillation dynamics, we may set up an Arduino sensing
module (Fig.2).
Fig.1 (a) Container attached to two springs in parallel (M-K), (b) Syringe fixed to the container, (c)
an outer boundary added to affect the local liquid motion (C); (d) Arduino Uno and supersonic
sensor module.
112-1 機械工程概論 Project A
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Department of Mechanical Engineering, National Taiwan University
112-1 ME 1010 Introduction to Mechanical Engineering
5 Tasks
Part A: Spring constant K
Individual spring
1. Hang a still spring in air and mark the original position of its end
2. Attach a mass of known weight W1, measure the displacement y1
3. Add counterweights W2, W3, ...; measure the corresponding displacements y2, y3, ...
4. Plot Ws on the x-axis and ys on the y-axis; fit a 1st-degree polynomial to the points
and find the slope to obtain the linear spring constant
5. Repeat for three times; obtain a mean K
6. Repeat for all the springs
Spring system
7. Attach two strings (of comparable Ks) in parallel configuration to your mass
8. Calibrate an effective spring constant Keff for the spring system, using Steps 1-5.
9. Make comments on the measured effective spring constant Keff and individual spring
constants K; does this agree to your understanding
Part B: M-K System
1. Hang M0 to the spring system, wait until it reaches force equilibrium; pull/release M it
2. Observe its vertical oscillation under this initial M0 and Keff.
3. Set up Arduino system to measure the displacement as a function of time (you may
use more than one sensor)
4. Analyze the data to estimate the amplitude A and the oscillation cycle T; does this
agree to what you already know about a simple harmonic oscillation? Why not?
5. Change M (M1, M2... Mn) and comment on how A and T change accordingly; make a
plot to show the trend; does this fit to your understanding?
Part C: M-C-K System
1. Fix the syringe to the original M-K system with (Mn, Keff); largest Mn
2. Place the storage box beneath the M-syringe-K system; test the oscillation amplitude
to make sure that the box does not interfere wit the oscillation process
3. Drill holes on the PP sheet and install L-shaped steel angle brackets
4. Roll the plastic sheet into a cylindrical tube and place it between the L-shaped brackets;
measure the tube diameter
5. Fill the storage box with water
6. Find the equilibrium position and introduce disturbance to the mass
7. Observe and measure how the oscillation is modified; compare the A & T to the values
found in B (easier to compare it on the displacement-time plots)
8. Change to a lower M; repeat steps C6-7
9. Now, change the radius of the outer cylinder (R1, R2, at least two, must creat
overdamping); repeat steps C6-7 and discuss how A & T change with Rs
10. Did you observe the transition from nearly SHM (negligible damping) to totally
damped response?
112-1 機械工程概論 Project A
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